The argument of direction, or slippery slope argument, is based on the device of stages and is used to counter the gradualist strategy. It is classified as an argument “based on the structure of reality” by Perelman Olbrechts-Tyteca.

1. The device of stages as a general action strategy

Generally speaking, the process of stages is implemented when the overall goal is judged as being directly unattainable; it is then divided into smaller, more easily achievable goals.
This process of division corresponds to a common action strategy, which is not necessarily manipulative. Experienced explorers explain that when lost in the desert, dying of thirst, and trying to reach a desperately distant town (final goal) one must set oneself a manageable goal, say the next dune, and then the next cactus, and so, step-by-step finally reach the distant town.

More relevant to everyday life perhaps is the solution to trying to carry a heavy weight. If I cannot carry this one hundred pound object, I dismantle it and carry each of its parts separately.
Such small but achievable goals might be ordered, as is the case in every learning process: one first learns to drive on a normal road for example, before learning to drive on an icy road. In these different cases, the actor keeps the ultimate goal in mind, in relation to which the partial goals are determined and organized.

2. The gradualist strategy

To get something from another person, an actor can apply the process of stages. In that case, the gradualist process should not be considered to be an argument but an intentionally opaque, manipulative strategy, S. Manipulation.

It is often found to be better not to confront the interlocutor with the whole interval separating the existing situation from the ultimate end, but to divide this interval into sections, with stopping points along the way indicating partial ends, whose realization does not provoke such a strong opposition. (Perelman & Olbrechts-Tyteca [1958], p. 282).

Step-by-step strategy, in this second sense, is commonly referred to in sales as a priming strategy:

The newlywed Joneses want to buy a flat; the real estate agent proposes a modest, fully sufficient two room flat, and they agree to buy it. Now the agent has got a foot in the door, and observes that very soon a baby will come; so they really need a three-room flat, and they change their mind and agree to buy one. But the agent observes that Mrs. Jones is developing a promising start-up, she needs an individual office; so they need a four-room flat, etc.

Arguing with the Lord to convince him to hold his wrath toward Sodom, Abraham uses such a priming strategy and step-by-step process — somewhat manipulative, but nonetheless laudable. The argument goes not from the few to the many but from just some to a very little few:

[…] Abraham remained standing before the Lord. Then Abraham approached him and said: “Will you sweep away the righteous with the wicked? What if there are fifty righteous people in the city? Will you really sweep it away and not spare the place for the sake of the fifty righteous people in it? Far be it from you to do such a thing—to kill the righteous with the wicked, treating the righteous and the wicked alike. Far be it from you! Will not the Judge of all the earth do right?”
The Lord said, “If I find fifty righteous people in the city of Sodom, I will spare the whole place for their sake.”
Then Abraham spoke up again: “Now that I have been so bold as to speak to the Lord, though I am nothing but dust and ashes, what if the number of the righteous is five less than fifty? Will you destroy the whole city for lack of five people?” “If I find forty-five there,” he said, “I will not destroy it.”
Once again he spoke to him, “What if only forty are found there?” He said, “For the sake of forty, I will not do it.”
Then he said, “May the Lord not be angry, but let me speak. What if only thirty can be found there?”He answered, “I will not do it if I find thirty there.”
Abraham said, “Now that I have been so bold as to speak to the Lord, what if only twenty can be found there?” He said, “For the sake of twenty, I will not destroy it.”
Then he said, “May the Lord not be angry, but let me speak just once more. What if only ten can be found there?” He answered, “For the sake of ten, I will not destroy it.”
When the Lord had finished speaking with Abraham, he left, and Abraham returned home.
Genesis 18:22-33 New International Version.[1]

Unfortunately, the Lord will not find ten righteous people in Sodom.

3. Argument of direction, or slippery slope argument

The term argument of direction is an alternative name for the slippery slope argument. It is used to prevent the application of a gradualist strategy:

“[it] consists, essentially, in guarding against the use of the device of stages. If you give in this time, you will have to give in a little more next time, and heaven knows where you will stop” (Perelman & Olbrechts-Tyteca [1958], p. 282).

[1] Quoted after www.biblegateway.com/passage/?search=Genesis%2018:16-33