Third Part Summary:
The man is scared, and thinks the old-timer was right: a trail-mate would be useful now in building a new fire. He sets himself to building it, aware that he is already going to lose a few toes from frostbite. With increasingly numb fingers, he grabs undesirable small twigs as the dog watches him.
The man reaches for a piece of birch-bark in his pocket, but his numb fingers cannot feel it. He fights off the thought that his feet are freezing, and beats his hands against his body to restore circulation. The dog watches him, and the man is envious of the dog's natural warmth. The man gets some sensation in his fingers, removes his mitten, and takes out a bunch of matches. But his fingers grow numb again and he drops the matches in the snow. His fingers are lifeless and cannot pick up the matches. Without the sense of touch, he uses vision alone to guide his fingers, and he "will[s]" them to close in on the matches.
He eventually bites a match and lights it on his leg. But the smoke goes into his nostrils and lungs, he coughs, and he drops it into the snow. He grabs the whole bunch of matches--seventy in total--and lights them on his leg, all at once. He holds them to the bark but soon becomes aware that his flesh is burning. Unable to bear it, he lets go, and the matches fall and go out into the snow. The bark is on fire, though, and he adds grass and twigs to it. In guarding the fire against pieces of moss from the grass, he scatters the twigs, and the fire goes out.
The man looks at the dog, and remembers hearing about a man who, caught in a blizzard, killed a steer and crawled inside its warm carcass. The man decides to kill the dog and puts his hands inside its warm body. He calls out to the dog, but something fearful and strange in his voice frightens the dog. The man crawls toward the dog, which moves aside. The man regains his composure and calls normally to the dog. When it comes forward, the man flails out at it, but his frozen, numb fingers cannot move. Still, he grabs the snarling dog in his arms. The man realizes he cannot kill the dog, since he is unable to pull out his knife or even throttle the animal. He lets it go, and it moves away from him. The man tries to restore circulation in his hands, but they are lifeless.
The man realizes that frostbite is now a less worrisome prospect than death. He panics and runs fearfully along the creek trail, the dog at his heels. Perhaps the running will restore his circulation. Even if he loses some fingers and toes, he might at least near his destination, where the boys could tend to him. He keeps blocking out the thought that he will soon die. He feels like his frozen feet are skimming across the surface. But his endurance gives out, and finally he falls and cannot rise. He decides to rest, then later walk. He feels warm within, although he has no sensation. He fights against the thought of his body freezing, but it is too powerful a vision, and he runs again.
He falls again, and the dog sits nearby and watches him, which angers the man. The man makes one last panicked run and falls once more. He decides he has been acting foolishly, and it would be better to meet death in a more dignified manner. He imagines himself with the boys tomorrow and coming across his own body. He imagines telling the old-timer that he was right.
The man falls off into a comfortable sleep. The dog does not understand why the man is sitting in the snow like that without making a fire. At night, it comes closer and detects death in the man's scent. It backs away, and later runs away in the direction of the camp, "where were the other food-providers and fire-providers."
Survival becomes the primary motivation for the man as he defends himself against nature. His increasingly desperate attempts to restore warmth to his freezing body contrast with the indifference of the Yukon. The environment merely remains the same--brutally cold--and does not care at all about the man's survival.
What is also significant within the environment is the importance of numbers. We already know that the temperature plays a crucial role, and that fifty degrees below zero demarcates the danger zone. The reader learns a new number here: seventy, the number of matches the man has. London could have simply kept stating that the man has a "bunch" of matches, but he tells us the exact number when they light. Time also plays a key role for the man, as does distance to the camp. Naturalism maintains that the world is knowable only through objective science. Hard facts, like degrees of Fahrenheit or the number of matches, make this particular world knowable.
The man finally takes these facts and makes conjectures about the future, unlike before where he refuses to think about processes. While he initially fights off ideas of his dying, he later engages in causal thinking, entertaining visions of his body freezing and even of finding his own body the next day, a truly abstract, futuristic mode of thought. But by now it is too late--projections of causal links will do little for him at this point.
His projections are pointless because whatever free will naturalism had afforded the man before (none, technically, but he could at least make decisions) has completely vanished by this section of the story. Hands are man's naturally selected advantage, and allow us to use tools, themselves the products of man's intellect. But here the man's hands betray him. He cannot operate the matches properly, nor can he use his knife, so both tools go to waste. In nature, his intellect turns out to be useless.
Instead, the dog's instinct prevails. It not only instinctively recognizes that the man is trying to deceive it some way, but its own naturally selected advantages--its fur coat, especially--keep it safe and warm. While the dog may not have the intellectual capacity to create fire and food for itself, it instinctively knows where the providers of these necessities are. In an indifferent, brutal environment, London maintains, this is a far more valuable resource than intellectuality.