In my 2017 Ketofest talk, I discussed some of the fallacies that beguile us in the nutritional realm. Platitudes and tropes, rhetorical cliches and quippy aphorisms can anaesthetise the mind against proper analysis of the complex, sometimes uncomfortable, always messy realities that confront us.

Dr Gary Fettke has to confront complex, uncomfortable and messy realities daily. It falls upon him to amputate limbs from diabetics. One day, he decided that his Hippocratic Oath demanded he suggest to his patients alternative strategies which may prevent or delay the necessity of such dismemberment. An angry dietary establishment denounced and oppressed him for this “appalling” behaviour, an oppression he bravely fights.

Gary investigated what lay behind the vehement, yet pseudoscientific, wordviews held by his oppressors. He sought the origins of much “common sense” modern nutritional thought, particularly that of the efficacy of a “plant based” diet. He discovered that these origins often lay more in religious dogma than in rigorous empiricism. Gary noted the profound effect the Seventh Day Adventist Church had on dietetics. This Church represents a specific case of what I discussed in my talk: the deeply “religious” impetuses behind our normative bases.

Even Fettkes can Flounder

We should never ourselves think that we, the enlightened few, cannot fall prey to the same beguiling faith-based fallacies. Even someone as perspicacious and brave as Gary. Let’s have a look at something he posted to twitter:

Gary posted “If it comes in a plastic bag and a cardboard box it’s not going to be real food“. Followed by the hashtags lchf (Low Carb, High Fat), jerf (which stand for “just eat real food”), and a final “food” hashtag for good measure.

At first glance, you may well find Gary’s homily reasonable. Not scientifical rigorous, certainly, but at worst a harmless rule of thumb? As much as I admire Gary, I cannot agree that such rules of thumb do no harm. Indeed, I feel we lie in the hideous nutritive predicament we do precisely because we allowed too many “common sense” “rules of thumb” to wash over us. Too many of us drowned.

Why Autopsy a Tweet?

We could simply accuse Gary’s meme of Begging the Question, of Appealing to Nature, and of instantiating a No True Scotsman fallacy (all of which it does), and call it a day; however, we have deplored the meme’s imprecision, so let us not fall foul of the same charge. Let us examine how it crumbles.

Arguments

At this point, let’s summarise what we mean by an “argument”, and the difference between a valid argument and a sound one.

In logic, an argument represents the stepping-stones  you take when trying to convince someone to accept a conclusion. We call these linked stepping stones of logic premises, one leading to another. Whatever the specific content of an argument, a system of logic allows us to determine whether that form of argument can ever provide useful answers or not.

We determine whether an argument has valid form by asking whether it must have a true conclusion if we find all its premises also true. If a form of argument can have all its premises true, and yet an untrue conclusion, then we have not created a valid form of argument.

Syllogisms: introduction

We can have many different and complex types of arguments, with many, many premises and complex formal notation to define and solve them. For now, though, let us examine one type of argument, called a syllogism.

This elegant little argument form first described properly by Aristotle has three propositions: two premises and a conclusion. One premise usually makes a general statement about the world. The other then makes a specific statement about something in the world that shares or avoids one of those general properties just defined. The conclusion then explicitly confirms what truth we can derive from the specific entity that shares this general property. Or does not.

A valid syllogism has a conclusion which necessarily follows from the premises:

An example of a valid syllogism:

• All men are mortal – True
• Socrates is a man – True
• Therefore, Socrates is mortal – True, because we determine both premises as true

If we determine Socrates belongs to the set of “men”, and we assign “mortality” as a property of that set, then we must conclude that Socrates inherits that property of mortality.

An invalid syllogism has a conclusion which does not necessarily follow from the premises. In Aristotelian logic, an invalid syllogism can no longer even have the name “syllogism”, but modern logic allows one to consider a three-pronged argument with a nevertheless wonky form!

An example of an invalid syllogism (if you can even call it one!):

• All men are mortal – True
• Socrates is mortal – True
• Therefore, Socrates is a man – Not necessarily true!

Here, we determine that both Socrates and Men lie in the same set, that of “mortality”; however, we cannot validly conclude that Socrates must also lie in the set of “men”, merely that he shares a characteristic also held by men – mortality. For example, perhaps this syllogism in fact discusses our prize pig, whom we named “Socrates”.

We call a valid argument with all its premises true a sound argument. A sound argument enjoys, in other words, both inherent structural integrity and contingent truth.

An example of a valid, sound argument:

• If black swans exist, then stating all swans are white is untrue – true
• A black swan exists – true
• Thus, stating all swans are white is untrue – true

An example of a valid, but unsound argument:

• If Atlantis exists, then modern maps are inaccurate – true
• Atlantis exists – false
• Thus, modern maps are inaccurate – false

Syllogisms: terminology

To help us to discuss the validity, or soundness, of a general syllogism, it helps if we can label the components that make up the premises and conclusions of that syllogism.

The Subject term

In a syllogism’s proposition, as in any sentence, the subject describes who or what we talk about. So in the proposition “Socrates is mortal“,  we have “Socrates” as the subject.

The Predicate term

A predicate term tells us something about the subject. It defines it further, or assigns it a property. So, in “Socrates is mortal”, we have “mortal” as a predicate of the subject “Socrates”. In the proposition “all sugars taste sweet”, we have “sweet” as the predicate of “sugars”. Note that we call a subject a “term”; we also call a predicate a “term”: any separately identifiable thing or idea we define a “term”.

Copulas and quantifiers

The “copulas” associate the subjects with the predicates, like the simple word “is“, or the verb “taste” in “all sugars taste sweet”. The quantifier includes words like “all” or “no“.

Categorical proposition

When you join a subject (“sugars“) with a predicate (“sweet“) via a copula (“taste“), and you filter it via a quantifier (“all“), you have put together a categorical proposition: in other words, a proposition which determines how X lies in the category Y.

Syllogisms: the major and minor premises

In a syllogism, we can divide the two premises into “major” and “minor”. To determine the major premise, we look at the conclusion.

The conclusion’s predicate represents the major term of the syllogism:

• Therefore, Socrates is mortal (we have the “mortal” predicate as the major term)

The conclusion’s subject represents the minor term of the syllogism.

• Therefore, Socrates is mortal (we have the subject “Socrates” as the minor term)

Now that we’ve looked at the conclusion, we can identify the major and minor premises.

Obviously, we identify the major premise as the only one containing the conclusion’s major term:

• All men are mortal (this major premise contains the conclusion’s major term)

And the the other premise, the only one that contains the conclusion’s minor term, we call the minor premise:

• Socrates is a man (this minor premise contains the conclusion’s minor term)

Finally, we have the middle term. The middle term joins the minor and major premises. Thus, it appears in both premises, but does not need to appear in the conclusion. Note that we can consider two middle terms as, effectively, one, even if they ppear in both singular and plural forms. In this case, “man” and “men” appear in both the major and minor premises, but not in the conclusion. Thus, we determine man as the middle term of the syllogism, that links the major to the minor.

 

Syllogisms: transformed into an enthymeme

So by now, you should have a basic idea of a syllogism. Things get surprisingly complicated, even with this little argument type, especially once you move into abstract notation, where you examine long argument forms, replete with negations, complex chains of quantifiers and so forth. Let’s leave things at this level for now: a syllogism, with a major premise, a minor premise, and a conclusion which shows how the premises validly conjoin.

So we have an idea what we mean by “syllogism”. What about “enthymeme”? The word “enthymeme” can mean a number of things, but in rhetoric, it names a syllogism where the speaker intentionally leaves out either the minor or major premises, or both, or even leaves out the conclusion.

Enthymeme: a syllogism without a major premise:

Enthymeme: a syllogism without a minor premise:

Why Make an Enthymeme?

Why on earth would we take a perfectly sound syllogism, and chop off one of its premises? Or leave the conclusion  hanging? Surely we want to show our working? Well, as part of making some pithy saying, or a meme, or a punchy speech, or a persuasive commercial, or any other sort of rhetoric, we might do it for effect. People have known, since the Ancient Greeks, that leaving out a premise and getting the audience to infer it lets them feel a little pleased with themselves. It’s like working out a tiny riddle.

Also, showing your working can make things seem a bit prosaic. After all, you want a punch and a conclusion, not necessarily punch, accountancy, and then prosaic conclusion.

Naughty Enthymemes

Sometimes, a rhetorician constructs an enthymeme because they suspect their audience might too quickly discover a complete syllogism’s lack of soundness (and perhaps even validity) if all its premises (or perhaps its conclusion) get an explicit airing. As with a magic trick, you don’t want the audience to have too long to look at it the mechanics of the illusion, lest they notice the wires, the fake finger or the forced card.

See a famous example of a somewhat obvious attempt at enthymeme naughtiness here:

We can see how an enthymeme allows a rhetorician to get away with making something that sounds logical, but actually fails the test when all its premises get revealed.

As  enthymeme:

• There’s smoke
• So there’s fire

Minor premise, conclusion. Bang, bang. Move on to the next topic and that little pithy observation lodges in the audience’s head, without any logical complications. Now let’s see what happens when we force the speaker to make the major premise explicit:

As  syllogism with its major premise restored:

• No smoke appears except when there’s a fire
• There’s smoke
• So there’s fire

Oh dear. With the reappearance of the major premise, the middle term smoke’s association with fire gets contextualised and limited. The rhetorician gives the audience an invitation – perhaps even the obligation – to falsify the first premise. And with its falsification, the whole syllogism dies. Even a child can think of plenty of times smoke appears without gross fire.

Let’s Eat Some Real Food Syllogisms

Gary has provided us with a number of propositions which tacitly slot into place as an enthymeme. In particular:

• If it comes in a plastic bag or a cardboard box, it’s not going to be real food (major premise)
  
• Humans should just eat real food (minor premise)

We can add a conclusion to that enthymeme, of course, so we have Gary’s Syllogism.

• Therefore, humans should not eat food that comes in a plastic bag or cardboard box (conclusion)

Let’s play around with the implications of Gary’s Syllogism:

• If it comes in a plastic bag or a cardboard box, it’s not going to be real food
• My supermarket sells cheese in a plastic bag
• Therefore, cheese is not real food

Hmm. Maybe some would be happy to agree that “cheese is not real food”. We haven’t said why we should “just” eat real food, though. Nor have we defined “real”. Let’s at least justify our claim that we should strive to eat real food, whatever we think that might vaguely describe, even if we do not tightly define it. What happens to cheese then?

• Humans only thrive eating real food
• Cheese is not a real food (we just proved it with Gary’s Syllogism!)
• Therefore, humans cannot thrive eating cheese

So, using Gary’s syllogism, and what initially seem some reasonable inferences therefrom, we have concluded that no human can thrive eating cheese. Oh dear.

Perhaps we should try the inverse of Gary’s Syllogism too. Whilst we do not necessarily have the right to do so, and in fact commit a Fallacy of the Undistributed Middle with our sleight of hand, we may as well see where it takes us, since we already find ourselves in the land of dodgy rhetoric in any case!

• All food sold unboxed and unbagged is real food
• My supermarket sells doughnuts loose
• Therefore, doughnuts are real food

Combine that with the previous syllogism:

• Humans only thrive eating real food
• Doughnuts are real food
• Therefore, humans thrive eating doughnuts

Hurray! “Logic” has proven we can eat doughnuts and thrive!

Who Gets to Define “Real”?

People will often suggest that reductio-ad-absurdum games as above bear little relation to “common sense” interpretations of “Just Eat Real Food” or the logical conclusions that one might make in determining how to act under that rubric. Not so! By not providing a specific,  concrete, water-tight, logically coherent definition for your little trope, you allow it to slip like quicksilver beneath any thumb that should act as its “rule”!

Don’t believe me? Then tell me you could never imagine this syllogism emanating from a vegan:

• Real food is only plant-based food
• Humans who eat real food are healthier, more ethical and environmentally sensible
• Therefore, humans should only eat plant-based food

You can argue until your face turns blue that your “real” trounces their “real” , but while you hoot and holler, carry on with things like:

• Real food is any plant-based food
• Tofu is a plant-based food
• Therefore, tofu is real food

You then continue your special pleading, and your no-True-Scotsman refinements. So you add a caveat that “real” food should receive minimal processing. We should consume it as close to its “unadulterated” or “natural” state as possible. Of course, this ignores the thousands of years of cultivation and hybridising, or the substantial “adulteration” that toiling and husbandry produces. But squint, and it seems we might have something. So the vegan continues:

• A real food is any food that receives minimal processing
• Cassava root usually receives minimal processing
• Therefore, cassava root is a real food

Ok. Let’s concede cassava’s status as a “real food”. As something that humans should covet instead of some “packaged” cheese? Think again. Nice, natural, real-food, unprocessed, unrefined cassava poisons hundreds of thousands of people a year.

If you highly refine cassava (perhaps thereafter putting it in a box, shock-horror, or bag), you can get it somewhat close to acutely-safe for human consumption. Let’s ignore the chronic hyperglycaemia and insulin spikes that these “real” foods provoke even when “safe”. So, you take a “real” food chock full of cyanide, you refine it substantially, and if lucky, you get a mediocre starch. Hey, what did we mean by JERF again?

So this “rule of thumb”, this clever little aphorism, this enthymeme come syllogism, when we unpack it, appears thus:

• Real food is [PREDICATE 1]
• Humans who eat real food are [PREDICATE 2]
• Therefore, humans should only eat real food

And, perhaps the inverse:

• Unreal food is [PREDICATE 3]
• Humans who eat unreal food are [PREDICATE 4]
• Therfore, humans must never eat unreal food

You decide what to fill in as PREDICATES. As does anyone who disagrees with you. As does the huckster snake-oil salesman. Good luck with any choral Kumbaya on that!

Still, at least you might actually try to fill in the blanks. Most ignore this ambiguous mess, sweep the “blanks” under the rug of tropey convenience. They want the seductive enthymeme to pretend to sing for itself. Just don’t listen too hard to the nonsense lyrics!

Rule of Thumb or Rule of Dumb?

So no, I cannot accept an illogical platitude as a useful rule of thumb. The same hand wags its finger at me for using the “highly processed” erythritol that comes in a plastic bag. With a label! Perhaps the rule of thumb even implies that I can no longer consider my tinned mackerel as “real food”; but perhaps the soy flour I can buy from the loose tub at my WholeFoods I can?

Snobby rule-of-thumb aside, I eat the mackerel nevertheless, and its proteins and omega-3 fats provide me with what I desire. I sweeten my home-made egg custard (made with eggs that come in egg-boxes and cream that comes in a plastic tub) with that erythritol, and add some vanilla extract, that comes in a boxed bottle. It provides me with a delicious, nutritious food that ensures I do not suffer hyperinsulinaemia. Perhaps it does it in an “unreal” way. My pancreas doesn’t care.

The rule of thumb has not helped me at all. Indeed, had  I followed it to its illogical inconclusions, I may just have felt ascetic guilt at the erythritol and confusion about the cream. I may have thought that unless I paid a lot at the fishmonger’s counter, I might as well just avoid fish because it transmorphed into some “unreal” by its processing and tinned vessel. You can tell me that you could never call processed erythritol “real food”. I don’t care. Not a jot.

I care about the simple metabolic realities that the molecules I place in my mouth engender. I do not care about Appeal to Nature Sentimentality. I do not care about Genetic Fallacy or Begging the Question of “realness”. And I refuse to allow you to beguile me with an enthymeme whose ambiguous fog shrouds the clear and properly logical tales of metabolic reality we should instead tell.