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Source: p 48, Syntax, A Generative Introduction (3 ed, 2012) by Andrew Carnie.
The following is NOT a homework question as I am not studying Linguistics but I have endeavoured to evidence my effort.

In section 1 of this chapter, it was claimed that we needed parts of speech to help us determine where in the sentence a word appeared. So for example, we know that verbs and adjectives in English don’t function as the subjects of sentences. Above we have given one test for part of speech category in terms of the word’s distribution in the sentence. Here’s something to think about. Have we created a circular argument: [1.] category determines position in the sentence and [2.] the position in the sentence determines category? Is this really circular? Does it matter?

[p 47 states:] The part of speech of a word is determined by its place in the sentence [ie: Position] and by its morphology, not by its meaning.

[2.] is true if only position, and NOT morphology, determines Syntactic Category.
So [2.] is false in general.

[1.] is false because Syntactic Distributions of different Syntactic Categories can overlap
(q.v. third paragraph, p 50).

But because a false premise implies anything, 1 ⇒ 2 and 2 ⇒ 1 are valid (but NOT sound) arguments. Ergo the argument above is circular. QED.       Am I correct?

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They're talking about section 1, not the complete set of all reality. This is called context. Presumably, the book goes on to explain why this rhetorical point is false.

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