Analysis: A Rulebook for Arguments - Ch. 6

In Weston’s sixth chapter, Deductive Arguments, he explains that “deductive arguments differ from the sorts of arguments so far considered, in which even a large number of true premises does not guarantee the truth of the conclusion (although sometimes they make it very likely).” [5]

In Weston’s first point of chapter six, Modus ponens, he deciphers what exactly is the structure of a traditional deductive argument:

“Using the letters p and q to stand for declarative sentences, the simplest valid deductive form is

If [sentence p] then [sentence q].
[sentence p].
Therefore, [sentence q].

Or, more briefly:
If p then q.
Therefore, q.”

This form is called modus ponens, and it’s important to note this specific structure because it can be used to develop deductive arguments. For example, we can use this structure or guide to create an argument of our own:

If drinking while driving causes more accidents, then drivers should be prohibited from being drunk, or being intoxicated, while driving. 

Drivers who are intoxicated while driving do cause more accidents.
Therefore, drivers should be prohibited from driving while intoxicated.

This form of argument allows us to see the two premises differently and separately to evaluate them clearly.

In the authors next point, Modus tollens, he wants to explain a second structure for deductive arguments:

If p then q.
Not q.
Therefore, not p.”

Essentially it is the same as the previous example of modus ponens, but this one, instead of being simply p or q, they’re not p etc.

In Weston’s twenty-fourth point introduces a third deductive form: “hypothetical syllogism.” This one is different from the other two because it has three factors and goes as follows:

If p then q.
If q then r.
Therefore, if p then r.

In this one, if p and q are equal, and q and the third variable are equal than that must mean that p and the third variable, r, are equal. An example can be, if I am getting really bad allergies then the pollen in the air must be high. If the pollen in the air is higher than usual, then it must be Spring. Therefore, if I am having worse-than-usual allergies then it must be Spring-time.

The next deductive form that the author introduces is “disjunctive syllogism”:

P or q
Not p.
Therefore, q.

Disjunctive syllogism, like the other deductive forms, is self-explanatory; it implies that if there are two options but if one is not the answer then it must be the other. Right? Well, Weston actually introduces the idea that, in the English language, there are actually two different interpretations of the word “or.” “Or” can either mean that at least one of p or q is true, and possibly both. In this sense, however, we are using “or” as an “exclusive” term, in which there must be one true between whether p or q is true.

Another valid deductive form is the “dilemma.” In which,

P or q
If p then r.
If q then s.
Therefore, r or s.

“Rhetorically, a dilemma is a choice between two options both of which have unappealing consequences.” [6] This is important to note because the “dilemma” deductive form demonstrates a situation in which a dilemma is proposed, so to speak. A simplified argument that Weston introduces in reference to Arthur Schopenhauer’s “Hedgehog’s Dilemma”:

“Either we become close to other or we stand apart.
If we become close to others, we suffer conflict and pain.
If we stand apart, we’ll be lonely.
Therefore, either we suffer conflict and pain or we’ll be lonely.” [7]

Although the example may be simple and brief, it truly covers the breadth the importance and central point of the “dilemma” deductive form.

In Weston’s twenty-seventh point, he introduces a traditional deductive strategy that is fundamentally apart of the modus tollens deductive form: reductio ad absurdum. In this one, however, instead of simply disproving the second option consequentially, we need to show that q is indeed false. “Arguments by reductio (or “indirect proof,” as they’re sometimes called) establish their conclusions by showing that assuming the opposite leads to absurdity: to a contradictory or silly result. Nothing is left to do, the argument suggests, but to accept the conclusion.” [8] This is important to note because the argument is fundamentally proving one variable correct, that there is no other conclusion other than that variable must be correct. The reductio ad absurdum form:

To prove: p.
Assume the opposite: Not p
Argue that from the assumption we’d have to conclude: q.
Show that q is false (contradictory, “absurd” morally or practically unacceptable...)
Conclude: p must be true after all.

Weston’s last point of chapter six is deductive arguments in several steps, “many valid deductive arguments are combinations of the basic forms introduced in Rules 22-27.” [9] Essentially, Weston introduces some methods of deciphering a larger argument into smaller increments to “decode” an argument more efficiently.

Side note: Sorry the format is extremely messed-up, but the fixing the deductive formats was becoming very tedious.

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