You have omitted a crucial part of the sentence:

... in the sense of §16.

The point is small objects admit canonical basepoints via the augmentation of the Weil algebras defining them. See this MSE question for the definition of $\operatorname{Spec}_R(\pi)$ for the augmentation $\pi:W\rightarrow R$. The author's definition only asks for pullbacks involving these canonical base points.

For the dual numbers, this notion does pick zero as a basepoint, since dual numbers can be identified with $R^2$ with-dual-number-multiplication, making the projection of $\bar x=(0,x)$ clearly zero.

You have omitted a crucial part of the sentence:

... in the sense of §16.

The point is small objects admit canonical basepoints via the augmentation of the Weil algebras defining them. See this MSE question for the definition of $\operatorname{Spec}_R(\pi)$ for the augmentation $\pi:W\rightarrow R$. The author's definition only asks for pullbacks involving these canonical base points.

For the dual numbers, this notion does pick zero as a basepoint, since dual numbers can be identified with $R^2$ with-dual-number-multiplication, making the projection of $\bar x=(0,x)$ clearly zero.

You have omitted a crucial part of the sentence:

... in the sense of §16.

The point is small objects admit canonical basepoints via the augmentation of the Weil algebras defining them. See this MSE question for the definition of $\operatorname{Spec}_R(\pi)$ for the augmentation $\pi:W\rightarrow R$. The author's definition only asks for pullbacks involving these canonical base points.

For the dual numbers, this notion does pick zero as a basepoint, since dual numbers can by identified with $R^2$ with-dual-number-multiplication, making the projection of $\bar x=(0,x)$ clearly zero.

You have omitted a crucial part of the sentence:

... in the sense of §16.

The point is small objects admit canonical basepoints via the augmentation of the Weil algebras defining them. See this MSE question for the definition of $\operatorname{Spec}_R(\pi)$ for the augmentation $\pi:W\rightarrow R$. The author's definition only asks for pullbacks involving these canonical base points.

For the dual numbers, this notion does pick zero as a basepoint, since dual numbers can be identified with $R^2$ with-dual-number-multiplication, making the projection of $\bar x=(0,x)$ clearly zero.