What maxim does Snowball use to simplify Animal Farm's seven commandments and why is it good propaganda?

Quick answer:

Snowball simplifies the seven commandments down to the maxim: "four legs good, two legs bad," a statement that makes for effective propaganda. In its simplicity, it is easily memorized and grasped by all the animals on the farms. In addition, it appeals to a shared sense of collective identity. It also introduces a hostile other that the animals need to unify against. This is a standard technique in propaganda.

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In the Gospel of Matthew 22.37-40, Jesus replies to the question of which are the most important of the Ten Commandments, saying:

Love the Lord your God with all your heart and with all your soul and with all your mind. This is the first and greatest commandment. And the second is like it: Love your neighbor as yourself. All the Law and the Prophets hang on these two commandments.

George Orwell clearly had this passage in mind when he had Snowball select the first two Commandments of Animalism as the most important, and condense them into the pithy dictum "Four legs good, two legs bad." This, in fact, reverses the order of the first two commandments, but it preserves their sense. It also encapsulates in the phrase "two legs bad" the principle behind the third, fourth and fifth commandments, all of which are about refusing to emulate human behavior. The phrase "four legs good" similarly stresses the same note as the sixth and seventh commandments, which stress the unity and brotherhood of all four-legged animals.

The phrase "Four legs good, two legs bad," therefore includes the central idea of all seven commandments in a simple phrase of six monosyllables. The grammatical parallelism of the slogan makes it easy to memorize, and lends itself to use as a chant, which is, in fact, how the animals often employ it. Under Napoleon's regime, this simple phrase is used in a sinister manner to drown out thought and nuance, until it is finally corrupted into "Four legs good, two legs better."

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When many of the less intelligent animals are struggling to memorize Animalism's seven commandments, Snowball reduces them down to a single statement: "four legs good, two legs bad." This, he says, expresses the essentials of those core principles, and would suffice to prevent an animal from falling back under human domination.

One of the reasons that this makes for such effective propaganda is its simplicity. In this, it provides a marked contrast with the more complex and nuanced seven commandments, which, themselves, could be understood as a simplification of Major's original vision. This simplicity allows it to be easily memorized by any animal on the farm, a theme expressed with the sheep, who become fanatical about reciting it, while also allowing for ease of understanding.

In addition to its simplicity, also note that this maxim is based in bifurcation. By dividing the world into humans ("two legs") and animals ("four legs") it instills in all the various animals a shared common identity, defining them collectively in opposition to their human antagonists. In this respect, you can see parallels to real world propaganda, which, likewise, often tends to appeal to a shared sense of common identity, for example, national or class identity, while often invoking an antagonistic other that needs to be opposed. These same techniques are present in Snowballl's maxim.

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Following the death of old Major, the pigs use his ideas regarding the rights of animals to develop a complete system of thought called Animalism. Under Snowball's leadership, the pigs create the Seven Commandments, which include tenets that promote the solidarity of all animals and prohibit certain human behaviors. Snowball and the other pigs then attempt to educate the animals on the farm by teaching them to read and write. Unfortunately, the majority of the animals are not able to grasp literacy.

Since many of the animals are unable to read the Seven Commandments and comprehend the tenets of Animalism, Snowball reduces the Seven Commandments into one maxim: "Four legs good, two legs bad." Snowball believes that the maxim contains the essential principles of Animalism and whoever grasps the concept will be safe from human influence. The simplicity of this maxim is an excellent propaganda technique because it precisely contains the essential meaning of the Seven Commandments in an easy-to-learn form, which every animal can remember and understand. It is so effective that the sheep, hens, and ducks constantly repeat the maxim throughout the day.

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Snowball tells the animals to remember "Two legs bad; four legs good."  This is an example of several propaganda techniques.

First, it represents simplification--taking a complex situation and narrowing it down to a clear-cut choice between good and evil.  The maxim forces the rest of the farm animals to see the humans as evil, implying that no human can have good intentions.  In addition to viewing the humans as their evil enemies, the farm animals see the pigs (or leadership) as their rescuers and heroes.  Like Hitler and his propaganda machine in Nazi Germany, the German people and farm animals do not question their leadership because they are led to believe that everything their leaders do is for their well being.

Secondly, the maxim represents assertion.  Snowball gives no specific evidence to support his claim that all two-legged creatures are bad or that the opposite is logical.  Because he knows that the farm animals are eager to follow, he makes it easy for them to do so, and they ask no more from him.

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