Why don't these types of arguments fall under the domain of logic?

Question

I'm currently reading a textbook on symbolic logic and it says the following which I find quite puzzling:

The province of logic as an exact science does not include all types of deductive reasoning, i.e., all cases of reasoning in which conclusions are deduced from premises, or in which inconsistencies or non sequiturs in arguments are exhibited. It is concerned only with instances of deductive reasoning that are correct or erroneous, valid or invalid, by virtue of their form alone, and by virtue of nothing else.

I have a few questions about this:

1. Why doesn't logic include "all cases of reasoning in which conclusions are deduced from premises". I thought this was the very mechanism by which a deductive argument operates, so shouldn't all arguments like this fall under the banner of logic?
2. Why doesn't logic include those arguments in "which inconsistencies or non-sequiturs" are exhibited? Isn't a non-sequitur an invalid argument i.e. an argument whose conclusion does not follow from its premises, thus should it not be included in logic?
3. Could the text be saying that deductive logic isn't concerned with actual examples/real instances of arguments, just the form? (I think is most likely it, but I need confirmation)

I think the exact science qualifier may have something to do with any misunderstanding. Could someone clarify what this passage means as its most likely that sonething has been lost in translation. Thank you.

Answer 1

Consider the following argument:

• Every apple is a piece of fruit. Therefore, if I have two apples then I have two pieces of fruit.

This is true "by virtue of form alone". For example, if I replace "apple" with any noun, and "piece of fruit" by any noun, then the argument is still logically correct (although the first sentence might become false).

For example, both of the following are logically correct:

• Every Ford Mustang is a car. Therefore, if I have two Ford Mustangs then I have two cars.

• Every cat is a piece of cheese. Therefore, if I have two cats then I have two pieces of cheese.

These have the same "logical form" as the original argument. I don't need to know what the nouns mean to evaluate the logical correctness of the argument.

Logically incorrect arguments

Now, here is an argument which is not correct "by virtue of form alone".

• My horse has a reddish brown coat. Therefore my horse is a chestnut horse.

That deductive argument is correct, in a common sense way, but only if I know what the words mean. It is not valid as a "logical argument" because it is not valid by virtue of "form alone". To make it logically correct, we need to add a hidden hypothesis:

• My horse has a reddish brown coat. Every horse with a reddish brown horse is a chestnut horse. Therefore my horse is a chestnut horse.

It is common to distinguish in this way between statements or arguments which are true by virtue of form alone versus statements or arguments that rely on the meanings of their words or on hidden assumptions. Logic, from a common point of view, is about the first kind rather than the second kind of argument. But, of course, people make deductive arguments of both kinds.

False hypotheses

Of course, in order to know that the conclusion of an argument is true, we need to know something about the words. It is common to say that the conclusion of an argument has to be true if the following both hold:

• The argument is logically correct, and
• The hypotheses are true.

This is supposed to be a sufficient condition for the conclusion to be true; it's not a necessary condition. From a certain point of view, "logic" is only concerned with the first bullet. The second bullet is also important, but not part of logic.

Answer 2

I think this part means just that the validity or invalidity of an expression, e.g. $a\Rightarrow b$ must be independent of additional assumptions c not stated in the expressions. Because otherwise we would never be able to evaluate whether an expression is true or false.

Answer 3

I think the author expressed his point a bit confusingly. He does not mean all cases in which "conclusions are deduced from premises" are excluded from logic. Instead, he means that only some cases in which "conclusions are deduced from premises" are excluded from logic. The cases that are included in logic are those in which validity is determined by their form alone.