The truth of the matter

Ostrich

Ostrich courtesy Krzysztof Niewolny

Most true statements are not absolutely true. They may be true enough for all practical purposes; true in some sense; officially true, but effectively meaningless; true, other things being equal; true, as far as it goes; or true in theory, but not in practice.

Generically, we can call these sort-of truths.1 Sort-of truth causes trouble for most brands of rationalism. In particular, the formal methods underlying logicism and probabilism both depend on absolute truth.

The fundamental principle of logical deduction is that it is absolute-truth-preserving. If all the inputs to a deduction (its premises) are absolutely true, then so will be the outputs (its conclusions). All the power of formal logic flows from this property. If “All ravens are black” and “Huginn is a raven” are both absolutely true, then “Huginn is black” is also absolutely true.

Unfortunately, formal logic does not generally preserve sort-of truth. Sometimes it does: if “All ravens are black” is pretty much true, inasmuch as they are all very dark gray, then “Huginn is black” will also be pretty much true. But if “all ravens are black” is pretty much true inasmuch as most ravens are absolutely black but a few are magenta, then “Huginn is black” might be entirely false. Sort-of truths don’t follow the standard rules of logical inference.

Could some other, more complicated logical rules work effectively with sort-of truths? The previous chapter contemplated adding the new truth value “sort of” to logic. This works formally, but doesn’t do much in practice. You can’t infer anything useful. As we saw, if you know that “all ravens are black” is sort-of true, you can’t conclude anything about specific ravens. And if “Huginn is black” is sort-of-true, it is also sort-of-false. You’d want to know in what sense is it true, and in what sense false.

“Sort of true” is not, in itself, sufficiently specific. There are many varieties of sort-of truths. It is true, by and large, that you can sit on chairs; and it is technically true that eggplants are berries.2 So, could we add these as additional truth values, and define inference rules for them?

It’s hard to see how that would work. Let’s try an example… If it’s officially but not actually true that ostrich licenses are issued for a term of two years (the local authority usually revokes them after a few months), and it’s more or less true that Antonia has just got an ostrich license (she applied for it under her late sister’s name to avoid a tax), how true is it that her license is valid for two years? This isn’t a logical question; it’s a practical and/or legal one. A correct answer depends on extensive, unstated knowledge of bureaucratic procedure. In practice, no one has succeeded in making a usable logic with values like “officially true” or “basically false.”

Unlike logicism, probabilism doesn’t require an absolute belief about what the truth of a statement is. However, it does require that any statement actually is either absolutely true or absolutely false. Suppose you want to know if there is any water in the refrigerator. To eliminate uncertainty, you look inside, and there appears to be only an eggplant. Now, is there water in the refrigerator? Well, with probability nearly 1.0, it’s sort of true that there is (in the cells of the eggplant).3 And with probability nearly 1.0, it’s sort of false (you were thirsty and there’s nothing to drink). It’s a rock-bottom principle of the mathematics that the probability of a statement being true and the probability of it being false have to add up to 1.0. (This is a different way of stating the Law of the Excluded Middle.) Here the probabilities of sort-of truth and sort-of falsity add up to nearly 2.0, which is uninterpretable as a probability. The math doesn’t work for sort-of truths.

For most rationalisms, these difficulties are sufficient reason to reject sort-of truths. Meaningful statements must be absolutely true or false—universally, objectively, independent of circumstances, purposes, or judgements—even if we don’t know whether they are true or false. (Then there is only epistemic uncertainty, and no ontological nebulosity.) However, outside of mathematics and maybe fundamental physics, there are few truths like that. The world of eggplant-sized objects just doesn’t work that way.

It’s not that rationalism couldn’t be true, in the abstract. It might work very well in some sort of world. Just not the one we live in. What sort of world? It would help a lot if all truths and falsities were absolute.

We want to know things about cottage cheese and dance moves and puppy training—but nothing is absolutely true about them. Obviously, all sorts of things are true about them, in a common sense way. But we can’t even say definitely whether or not something is cottage cheese. There are always marginal cases, like cottage cheese that has been in the refrigerator too long and is gradually turning into something else. Nor is it absolutely true that cottage cheese is white. That is only “more-or-less true”; examined closely, it’s slightly yellowish.

Somewhat less obviously, absolute truths are rare even in the professional practice of rational, technical disciplines. Moreover, this is rarely a problem. Mostly-true truths are usually good enough, and we routinely reason with them effectively.

  • The Don’t Repeat Yourself principle is mainly true in software development.
  • Medicinal chemists know to avoid molecules above 500 daltons, because it is mostly true that they are too big to be “druggable.”
  • Probability theory is often useful in practice, even though (as we’ll see later) the scarcity of absolute truths and the ubiquity of unknown unknowns make it almost never officially applicable.

One way we make rationality work is by making mostly-true truths even more true, by engineering regularities into materials, objects, processes, and social structures.

Quixotic quests for absolute truth

Holy Grail

Encountering a sort-of truth, rationalists often say “there must be an absolute truth somewhere in the vicinity; we should find and use that instead.” I’ll describe four strategies for converting sort-of truths into absolute ones: here briefly, and in detail in later chapters.

Each of the four methods works in some cases. Indeed, these moves are all meta-rational: they are methods of ontological remodeling, intended to make rationality work better. Unfortunately for rationalism, they provide no general solution, either individually or in combination. Commonly, none of them can generate absolute truths that are usable in practice.

Also, they are often impractically expensive when they do work. Locating an absolute truth may be difficult; the true statement may be unreasonably complicated; using it in practical inference may prove intractable. As a practical matter, you have to weigh the potential value of absolute truth, for enabling truth-preserving formal inference, against these costs.

As discussed earlier, rationalism tends to misinterpret nebulosity as linguistic vagueness or as epistemic uncertainty. The first two strategies for producing absolute truths correspond to these two misinterpretations; the third and fourth tackle the underlying ontological problem.

Treating the problem as one of linguistic vagueness, the first strategy tries to define all the terms in a statement with absolute precision, so that it becomes absolutely true or false. This proceeds in two steps.

  • First, you move the nebulosity inside the statement. If it’s more-or-less true that cottage cheese is white, then perhaps it’s absolutely true that cottage cheese is more-or-less white. But this by itself doesn’t help with deduction. It’s not clear what “more-or-less white” means, or what you can legitimately infer from it. Also, even though it is more-or-less true that cottage cheese is white, it’s not absolutely true that cottage cheese is more-or-less white. If you mix blue food coloring into cottage cheese, it’s not white at all, but it remains more-or-less cottage cheese.

  • So a second step typically requires splitting the meaning of the terms into technical special cases that are defined differently. For example, one might define exactly the range of reflective properties that count as a particular kind of whiteness specialized for cottage cheese. And one might define exactly the range of substances that count as cottage cheese, deliberately excluding some that mere laypeople, who are not professional cottage cheese definers, would ordinarily accept (such as mixtures with food coloring). The next chapter of the book, “Are eggplants fruits?”, discusses this strategy.

Alternatively, treating the problem as one of epistemic uncertainty, the second strategy reinterprets the mostly-true statement “all ravens are black” as an absolutely true statement that “the probability that a raven is black is high.” This sometimes works well: when variation is genuinely random and the entities involved are otherwise uniform, so a general statement is adequate.

But in individual one-off cases, you usually want to know why exceptions occur; variations are patterned and meaningful. “Don’t Repeat Yourself” and the chemist’s 500-dalton rule of thumb are not “true with a given probability.” Every bit of code and every potential drug is meaningfully unique, and individual exceptions to the rules have to make specific sense in context.

If you observe that “Alain is bald” is pretty much true, that is not equivalent to “Alain is bald with high probability.” It’s about your friend Alain, not people in general. It’s not that you have imperfect certainty about whether or not he is bald. You know how bald he is; the issue is that he’s not altogether bald. The chapter “When will you go bald?” discusses this further.

Just how bald is Alain? Can we put a number on it? Then we could get absolute truths about whether some people are bald or not, and absolute truths about the degree of baldness in marginal cases. Maybe “Alain is 73.84261% bald” is absolutely true. Or maybe truth itself a matter of numerical degree, so “Alain is bald” is 0.7384261 true. “When will you go bald?” discusses these ontological strategies (numbers three and four) too. They may work when nebulosity is a matter of “shades of gray.” Most nebulosity doesn’t work that way, though.

As you may already agree, none of the four strategies is individually adequate to absolutize all cases of sort-of truth. But maybe there are just four different forms of nebulosity, so every sort-of truth could be handled by one of them? Or if a handful of additional methods were added? I think that, after reading on, you will find this unlikely. Proving that as an in-principle, philosophical point is not part of the program here, though.

Rather, in the actual practice of technical rationality, absolutizing sort-of truths is not generally necessary, or even common. An adequate account of rationality needs to explain how this can be.

Part Three of The Eggplant is about that. How do we reason formally without the absolute truths that formal reasoning methods formally require?

Rationality treats selected sort-of truths as if they were absolutely true. How can we get away with this deceitful fantasy? Some rational inferences turn out to be reasonably true. That is, they count as true enough under reasonable (non-rational) interpretation in a specific context.

For this to work, we have to choose carefully which sort-of truths we will treat as absolutely true. We have to know, or reason about, which formal inferences we can get away with—even though, starting from only-sort-of truths, they are not logically sound. We have to know, or reason about, how to translate our formal conclusions back into sort-of truths, and into reasonable actions. All these are central meta-rational considerations.

  • 1. The term “partial truth” is more common in philosophy. For an in-depth discussion, I recommend Elijah Millgram’s Hard Truths. He takes much the same positions I do here, and discusses the issues in much greater detail, with many fun examples.
  • 2. “In botany, a berry is a fleshy fruit without a stone produced from a single flower containing one ovary. Berries so defined include grapes, currants, and tomatoes, as well as cucumbers, eggplants (aubergines) and bananas, but exclude certain fruits commonly called berries, such as strawberries and raspberries.”—Wikipedia. Who knew?
  • 3. Probabilists insist that no belief should have probability 1.0. There’s always the possibility that what you saw wasn’t a real eggplant, but a plastic imitation.

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This page is in the section Part One: Taking rationalism seriously,
      which is in In the Cells of the Eggplant.

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