Conjunctive and disjunctive assertions

Question

I am a new learner to logic and philosophy, after spending some time reading Introduction to Logic by Copi, Cohen & McMahon, I'm stuck on this matter... please help me so I can read forward...

The Amazon Basin produces roughly 20 percent of the Earth’s oxygen, creates much of its own rainfall, and harbors many unknown species.

This sentence simultaneously asserts three propositions, concerning what the Amazon Basin produces and what it creates and what it harbors. The passage thus constitutes a conjunctive proposition. Asserting a conjunctive proposition is equivalent to asserting each of its component propositions separately.

Some compound propositions do not assert the truth of their components. In disjunctive (or alternative) propositions, no one of the components is asserted. Abraham Lincoln (in a message to Congress in December 1861) said, “Circuit courts are useful, or they are not useful.” This disjunctive proposition is plainly true, but either one of its components might be false.

I am genuinely confused by that last two paragraphs. What does it mean by "asserting each component separately of a compound conjunctive proposition" and "nothing is asserted in compound disjunctive proposition"?

Thank you

Answer 1

The "meaning" of the logical connective are defined by the rules of inference governing them.

For conjunction ("and") we have :

(φ∧ψ) ⊢ φ and (φ∧ψ) ⊢ ψ;

for disjunction ("or") we have :

φ ⊢ (φ∨ψ) and ψ ⊢ (φ∨ψ).

The first couple of rules formalize the fact that :

"Asserting a conjunctive proposition is equivalent to asserting each of its component propositions separately."

But for "or", we have no rule like :

(φ∨ψ) ⊢ φ.

This correspond to :

"In disjunctive (or alternative) propositions, no one of the components is asserted."

In other words, the assertion of a disjunction does not license us to assert its disjuncts separately.

If we know that an "alternative" between two possibilities holds, not necessarily we are able to know which between the two holds.

Answer 2

What does it mean by "asserting each component separately of a compound conjunctive proposition"?

It means to asserts that each of the component statements is true. In the example one asserts

• that the Amazon Basin produces ... and
• that the Amazon Basin creates ... and
• that the Amazon Basin harbors ... .

What does it mean by "nothing is asserted in compound disjunctive proposition"?

The claim from the quote is a bit unprecise. A proposition is disjunctive if and only if it is composed of two or more statements connected by or.

Apparently, the example presents a disjunctive proposition. Even more, it is the special case of two component statements where each is the opposite of the other. In formal terms "A or B" with B = non A.

According to 2-valued logic either "A" is true or "non A" is true. And a disjunctive statement is true if and only if at least one of its components is true. Hence by trivial reason, the compound statement " A or non A" from the example is true. But that does not give you any information. Because the compound statement is true due to formal reasons alone, independent from the content of "A", i.e. nothing is asserted.

But a general disjunctive proposition, e.g., "He came yesterday or the day before" makes a positive assertion: 1. He came and 2. It was on one of two possible days.