Leaf should have written: "formal fallacies". All formal fallacies are non-sequiturs.

But the arguer has no business assuming either 3 or 4, and does so only if he already has accepted 7. And, you are right. Neither 3 nor 4 are "steps" in the argument. Both are premises, and 3. is there only so that the conclusion can be drawn. And that is why it begs the question. It violates Aristotle's prescription that the premises should be better known than the conclusion.

circular reasoning, reasoning that, when traced
backward from its conclusion, returns to that
starting point, as one returns to a starting point
when tracing a circle. The discussion of this topic
by Richard Whatley (1787-1863) in his Logic
(1826) sets a high standard of clarity and pene-
tration. Logic textbooks often quote the follow-
ing example from Whatley:

[INDENT]To allow every man an unbounded freedom
of speech must always be, on the whole,
advantageous to the State; for it is highly con-
ducive to the interests of the Community, that
each individual should enjoy a liberty per-
fectly unlimited, of expressing his sentiments.[/INDENT]

This passage illustrates how circular reasoning is
less obvious in a language, such as English, that,
in Whatley's words, is "abounding in synony-
mous expressions, which have no resemblance
in sound, and no connection in etymology." The
premise and conclusion do not consist of just the
same words in the same order, nor can logical or
grammatical principles transform one into the
other. Rather, they have the same propositional
content: they say the same thing in different
words. That is why appealing to one of them to
provide reason for believing the other amounts
to giving something as a reason for itself.
Circular reasoning is often said to beg the ques-
tion. 'Begging the question' and petitio principii
are translations of a phrase in Aristotle con-
nected with a game of formal disputation played
in antiquity but not in recent times. The mean-
ings of 'question' and 'begging' do not in any
clear way determine the meaning of 'question
begging'

There is no simple argument form that all and
only circular arguments have. It is not logic, in
Whatley's example above, that determines the
identity of content between the premise and the
conclusion. Some theorists propose rather more
complicated formal or syntactic accounts of cir-
cularity. Others believe that any account of cir-
cular reasoning must refer to the beliefs of those
who reason. Whether or not the following argu-
ment about articles in this dictionary is circular
depends on why the first premise should be
accepted:

[indent]
(1) The article on inference contains no split
infinitives.
(2) The other articles contain no split infini-
tives.
Therefore,
(3) No article contains split infinitives.[/indent]

Consider two cases. Case I: Although (2) sup-
ports (1) inductively, both (1) and (2) have solid
outside support independent of any prior accep-
tance of (3). This reasoning is not circular. Case
II: Someone who advances the argument accepts
(1) or (2) or both, only because he believes (3).
Such reasoning is circular, even though neither
premise expresses just the same proposition as
the conclusion. The question remains controver-
sial whether, in explaining circularity, we should
refer to the beliefs of individual reasoners or only
to the surrounding circumstances.
One purpose of reasoning is to increase the
degree of reasonable confidence that one has in
the truth of a conclusion. Presuming the truth of
a conclusion in support of a premise thwarts this
purpose, because the initial degree of reasonable
confidence in the premise cannot then exceed
the initial degree of reasonable confidence in the
conclusion.

See also INFORMAL FALLACY, JUSTIFICA-
TION.

Right. Take a few examples of formal fallacies:

Affirming the consequent:
1. P→Q
2. Q
3. :. P

"Argument from fallacy":
F: x

"Argument from fallacy":
F: x