Introduction
The science of logic is properly considered a discipline of mathematics, and a foundational one, at that. Indeed, logic is the essential tool for determining which mathematical ideas actually hold under scrutiny — every technique of mathematical proof ultimately boils down to an application of logic. As mathematics are generally seen as providing the “hardness” that makes the “hard” sciences…well, hard, this is pretty important. Mathematics are often described as the “language of the Universe” or, in a more bygone age, as the “language of God”[1] — so crucial to our interactions with the world around us that we’d better be damned sure that, when a mathematician tells us something is the case, we’re confident that he isn’t just jacking off in our faces.
It is somewhat ironic, then, that logic[2] has very little to do with whether or not a particular statement is actually, you know, true. It doesn’t even bother defining what truth is, only how it works. That is, logic gives a set of tools for putting general truth-bearing statements together and being able to guess what the truth value of the resultant statement is, depending on the truth values of the statements which make it up. Logicians leave proving the actual truth of particular statements to other mathematicians[3], and a definition of what it even means for something to be true to philosophers — who in turn seem to have abandoned the search for truth entirely in preference for classifying precisely into which schools of philosophy certain brief aspects of previous philosophers’ arguments fall.
Lately I have been curious about how truth operates in a less technical way, or at least how most people usually relate to truth in their lives. I am especially interested in how people justify their attempts to control others by claiming special knowledge of the truth, or that a given truth says more than it probably does about the world and the correct way to live in it. Like far more worthy logicians and philosophers before me, I will leave the task of questioning what the truth is to Oprah (at least for now), and instead get on with the grubby business of trying to figure out how the truth works.
First things first, I’ve used the term “statement” five times[4] already without bothering to let you know how logicians use this word when studying the mechanics of truth. The technical definition of a logical statement is quite specific, and bears only a passing relationship to its common usage in English (as well as, sadly, in German[5]).
A statement is any sentence that can be considered true or false (even if nobody knows which is which in practice). In particular, this excludes all questions, greetings, remonstrations, and imperatives. On the other hand, it includes the answers to questions, declarative statements, explanations, and advice of the “if you want X to happen, you should do Y” variety.
“Tim wears daisies in his hair when it rains” is a statement; it can be either true or false, and might even change from one to the other depending on any number of factors. “All Yeblorbs are also Zurblabs, but not all Zurblabs like Tweeloogs, and if Tweeloogs ever like Yeblorbs then Zurblabs as a whole will declare war on Upper Tweeloogia” is also a statement[6]. “Go to your room” is not a statement.
When you think about it, most of the sentences we actually care about — in casual conversation, a scientific paper, a news broadcast, a history lesson, or a rambling blog post — are statements of one kind or another. Our beliefs about the truth or falsity of a given statement influence how we behave; other peoples’ beliefs about statements influence how we treat them. In pretty much every society, professing belief in particularly unpopular statements comes with some degree of social risk; in some societies, acknowledging belief in the wrong statement can cost you your freedom, or your very life.
And therein lay the rub; logical statements are not simply the basic elements of the science of logic, they are also the building blocks of belief — every belief is, at its root, an assertion that a particular statement is, in some sense, true. And belief is powerful, perhaps the most decisive element of the human psyche[7].
Three Kinds of Truth
By my reckoning, most belief-motivating statements fit into one of three “senses” in which they are true. Let’s call these senses physical truths, personal truths, and social truths.
A physical truth is something that is true or false regardless of whether we believe in it, or indeed whether we even know there’s anything to believe in at all. This obviously includes almost all of the true things we investigate with the so-called “hard” sciences, but also much else besides — in fact, almost everything[8] that is true is true in this physical sense.
A personal truth is a statement about one’s internal state, experiences of the world, reactions to stimulus, opinions, personal values, taste, aspirations, fears, appetites, etc. The relatively newfangled obsession with finding just the right boutique identity labels mostly has to do with developing — or, less often, discovering — what sorts of personal truths are most important to you, and what their truth values may actually be.
A social truth is something that is true or false if enough of the right kind of people insist it is. Laws, mores, customs, public policy, fashion, the particular meanings of a word at any given time, institutionalised or ubiquitous religious beliefs, international relations, and the application of most sciences[9] are prime examples of social truths.
It is worth noting that a statement is distinct from a phenomenon — a rock is a thing that exists outside of truth, and indeed has an uncountable number of physical truths associated with it. If the rock is revered, such as the Ka’aba, it has a whole host of social truths associated with it as well. If it’s part of a piece of jewellery, it can have many deep personal truths attached to it. There are also limitless examples of social and personal phenomena which all have truths in each of the three senses under consideration.
It is also worth noting that there is a fair conceptual distance between physical truths and the other kinds; social and personal truths, while clearly distinct, are much more similar to one another than they are to physical truths. A certain kind of hard-nosed skeptic[10] may even claim not to recognise non-physical truths as having any actual truth-bearing quality at all, though whether or not he calls them “truths” has little impact on his having to navigate and negotiate them anyway.
The truth value of a physical statement does not change depending on what a society or an individual believes about that statement; an individual, or everyone in the world, could insist that gravity did not exist or the speed of light were variable or that they were not human beings or that SARS-COV-2 weren’t real or that it were actually possible for a human being to change their physical sex, and this insistence would not make any of these things true.
The easiest way of appearing to change the value of a physical truth is to play games with the meanings of words — that is, you could change the social truths pertaining to the underlying phenomena, and get everyone to use different terms to explain the physical truths, but the values of those physical truths would not be altered. The only way for human beings to actually influence the values of physical truths is to get our hands dirty, develop technologies which let us play certain physical truths off of each other to get a desired result, and build up social truths about the applications of those technologies which makes them ubiquitous — and even then, some social-truth compromise is usually required[11].
Unlike physical truths, which require no police or armies to enforce, social truths must be actively realised by the cooperation of human beings. They are enforced, in the worst case, by armed men who will imprison or kill you for failing to uphold them. In most cases, though, these truths are enforced by looks, or gestures, or any of a million little decisions that people make — whom to trust, or promote, or hire, or befriend, or shun, or marry — often without an overt conspiracy of thought. Because we are social beings, we are tuned to sense others’ approval or opprobrium, and we have a strong instinct to adjust our behaviour accordingly, even if we don’t consciously understand why.
Personal truths are largely maintained by some combination of repetition, attention, diligence, neurochemistry, and deep-rooted lessons learned early from trustworthy or otherwise-unignorable sources. And though we often like to think that our personal truths are fixed in some way — that we discover rather than develop who we are — this is usually not precisely the case.
That is not to say that personal truths are always, or even mostly, matters of whim; most people do not consciously decide a favourite colour, or flavour of ice cream, or musical genre, or their sexual proclivities. Plenty of religious converts and atheists insist that their spiritual change of heart occurred without conscious direction, and sometimes even against their better judgement.
Nevertheless, the truth value of a personal truth can often be changed through conscious effort or further exploration — a lazy person can become hardworking (or vice-versa), you can be convinced of the non-existence of God, a picky eater can discover a wide variety of dishes they actually enjoy, a sexually vanilla person can discover or develop an interest in kinky sex, and even someone who believes they are entirely hetero- or homosexual may find someone of an incompatible sex whom they nevertheless enjoy fucking. Sometimes a change in a personal truth comes from the person having been mistaken, or from a response to some ill-learned lesson, but more often this change comes from the hard work of making different decisions time and time again.
Truth to Power
Not all truths are created equal. In particular, owing to their self-enforcing nature, physical truths have an aura of authority to them that the other two lack. Societies and individuals thus have every incentive to frame their own truths as physical truths, as any individual or any society which acts too long in defiance of too many physical truths will usually get their comeuppance as a matter of course[12].
This instinct is helped immensely by the indelible fact that we are all of us physical beings, flesh and blood individuals. And, until AI emerges and kills us all, every society is composed of just such individuals acting in concert. In other words, every single individual or social truth is based upon a foundation of uncountable physical truths; this genetic relationship can be, and often is, misused to reframe metaphysical truths as physical truths in disguise.
The habit of justifying or enforcing metaphysical truths by recourse to physical truths (or, more often, claiming that what appear to be metaphysical truths simply are physical truths) has such a long pedigree that logicians refer to it as an appeal to nature (which is often mistaken for the related naturalistic fallacy)[13].
Philosophers and politicians since time immemorial have cast their ideas and ambitions as flowing from nature, or from Nature’s God, or the Cosmos, or what have you — in times of paganism, of theocracy, and of post-Enlightenment social democracy, many successful policies and cultural phenomena have been enacted (or ended) by recourse to what I have dubbed physical truths. Most modern social movements are at least somewhat based on this tactic, and to the extent they are, they have generally been successful in both capturing attention and in convincing a critical mass of the public of their cause.
The most successful of these within the last few decades has to be the public acceptance of homosexuality. Twenty years ago, homosexual activity between men was illegal almost everywhere in the world, and in none too few countries across the West. Men were prosecuted for these crimes within living memory, sometimes within my own lifetime. George Bush’s last (and, incidentally, his first) legitimate presidential election victory came on the back[14] of scaremongering homophobia; four years after that[15], the citizens of the Socialist Republic of California voted to have their state’s constitution say explicitly that marriage was only for one man and one woman forever (or at least until one of them decides to get lawyers involved).
From those heady days of Californians upholding the values of traditional marriage, we have arrived at a social landscape largely beyond the wildest dreams of the most fervent John Kerry supporter. Not only is gay marriage legal in all fifty of the United States and virtually the rest of the West, in most of the same places it is culturally (and occasionally legally) unacceptable to utter the wrong opinion about this fact in public. We have two months straight[16] of corporate-sponsored Gay Pride celebrations in every major city from Perth to Stockholm every year, and the new rainbow flag is steadily colonising the very halls of spiritual and temporal power which only too recently inveighed against its simpler predecessor[17].
All this within two decades, after centuries of Western suppression of homosexuality, of it being generally recognised as a spiritual aberration or a mental illness, practised at risk of social censure, torture, and death. (Oh, and the fear of eternal damnation, I guess.)
How did we get here? How did this deep social truth change in such a breathtakingly short span of time? By and large, it was a combination of two somewhat-contradictory streams of activist thought which chipped away at social reticence for recognising (or even allowing) public homosexual relationships.
The first, and generally least recognised, was the relentless pro-marriage activism from lonely conservative gay men (of whom Andrew Sullivan is the archetypical example) which argued that the fundamental conservatism of marriage as an institution would have a civilising influence on homosexuals (especially homosexual men) that lobotomies, electroshock therapy, getting dragged to death behind pickup trucks, or spending decades in prison had not. “If you can’t beat them, let them join you” is a good summation of this line of activism.
The second line of reasoning, which looms larger in our collective memory in the years since 2015, was emblazoned (though not invented) by Lady Gaga just a few years after the California plebiscite effectively rendering public recognition of homosexual marriages unconstitutional. “Born this way”, and its predecessor chant “We’re here, we’re queer[18], get used to it!” are nothing less than an assertion of a physical truth, and the insistence that this physical truth completely overthrow the then-regnant social truths associated with homosexual relationships.
This assertion, and its implication, won out in a stunning social revolution whose consequences are still reverberating. We may well explore some of those consequences and follow-on social developments at a later time, for better and worse, but for now let’s just let the homosexual revolution of the early twenty-first century serve as a very successful illustration of a more general point.
We should probably get much better at holding physical truths apart from social and individual truths, and we should probably be much warier when someone uses physical truths to justify making social (or even individual) changes. This method, as all methods of politics, is blind; people you hate will learn to master it, perhaps better than you, and use it to push for social truths you despise. After all, all those centuries of homosexual oppression were themselves justified by assertions of physical truth and the supposed negative consequences of allowing people to defy said truths.
Is the next social revolution that basis itself in physical truths and uses appeals to nature going to be like the homosexual revolution, or more like the Social Darwinists’ abortive campaign of euthanasia (or their much-more successful, or at least more perniciously long-lived, campaign of retroactively justifying race-based slavery)?
I don’t know, but I hope we can figure out how to find out.
[1] Galileo Galilei is supposed to have said “Mathematics are the language in which God has written the Universe.” The small University I attended for my initial degree began as a religious institution for women, and back then its mathematics department was seen as second only to theology in the institution’s hierarchy of prestige. By the time they allowed non-female and non-Christian matriculations, the department’s esteem had been somewhat overshadowed by the preponderance of psychology and education courses which attracted much of the student body, but the mathematics department nevertheless retained a certain aura of detached confidence that the other departments largely lacked.
[2] Like most disciplines of mathematics, there is an ambiguity between the overarching discipline of logic, the class of “logics” which mathematicians play with according to slightly-different assumptions or rules, and the member of that class that most mathematicians who do not specialise in logic actually encounter (i.e., first-order predicate logic). For the purposes of this meditation, I am mostly referring to first-order predicate logic in this introduction, though it doesn’t really matter to the exploration that much.
[3] To be fair, logic is hardly alone among mathematical fields for leaving its most basic elements inferred from common usage rather than rigorously defined. Anyone who has learned anything about geometry will have heard that Euclid’s Elements do not bother to define what a point, a line, a plane, or even a space is. Pretty much all mathematical disciplines are like this, unable to actually pin down just what it is they are talking about. And if the Queen of the Sciences and the Language of God has this feature, you can bet that all other sciences and pseudo-sciences are like this as well. I will probably ramble about the implications of this on our ability to actually know things at some other point.
[4] Six, now, I guess.
[5] Das Statement is a prime example of modern Denglish, upon which I’ve already briefly remarked, and hope to write more extensively on at some point in the near-ish future.
[6] An admittedly insane one, but it still counts.
[7] Beliefs not only impact how we treat one another, but even how we feel about ourselves; the placebo effect seems to be quite real, and anxiety disorders are really just extreme fixated beliefs.
[8] In the mathematical sense of “almost everything”. The facetious way of proving this is to observe that the statement “X is a social/personal truth” is, itself, a physical truth; thus there are at least as many physical truths as there are social and personal truths put together, plus all the truths of the physical arrangements of all the matter in the Universe, of which there are a bajillion million times infinity all plus one for every piddling social or personal truth you can dream up.
[9] I once got into a tedious discussion in an Astral Codex Ten comment section (LINK TO THIS) about whether blood typing systems are “arbitrary social constructions” or not, with at least two apparently-smart people willing to go to bat to answer the question in the affirmative because different medical traditions have developed different blood classifications. If I had that argument to do over again, I would say that a given blood typing system is a social truth, while the question of a given transfusion’s likelihood of killing you is a physical truth.
[10] As you may be able to tell from this post’s title, I have been this sort of skeptic before, and may become one again, withal.
[11] “People can’t fly” was a true physical statement until planes were invented in the early 1900’s; “a person cannot fly” is still broadly true, though a few jetpack prototypes have shown some promise. But it is actually still true that people cannot fly unless they get together and dig up aluminum and petroleum and some other trace materials, put them together in very specific ways, and herd into the resultant tubes and trust the engineers and maintenance workers and pilots not to fly them into the ground.
[12] Unless society at large has enough spare abundance to tolerate a certain number of crackpots, but even then, if the crackpots take over, that abundance usually disappears and the society ceases to exist, or at least undergoes a radical transformation.
[13] Arguably what I’m talking about here is not, strictly speaking, an appeal to nature; it isn’t so much people going “X is natural, therefore good”, but rather “X is natural, therefore not enforcing X socially will lead to bad outcomes”. I think this is a distinction without a great amount of difference.
[14] Pun not intended, but left in once noted.
[15] The same day Barack Obama won his historic election (during which he felt the need to pretend to find gays getting married icky).
[16] Pun somewhat intentional.
[17] Here in Europe, capitals are still mostly festooned with the old-school flag, but the activist children filtering the new American religion will surely correct their governments’ unacceptable genocidal transphobia presently.
[18] Yes, darlings, the elders who helped liberate homosexuals used “the Q-slur”.