A Logic question?

Question

True Statement: 1 in 16 jaguars are black (the animal)

Assuming the above statement is true, is the following statement also true?

Jaguars are black.

I know that it implies that ALL jaguars are black, but according to formal logic, would that assumption be considered in determining whether this statement is true or not. It obviously is true that SOME jaguars are black, so does that translate to mean that Jaguars are black, when there is no specifier as to the set of jaguars that is being referred to here? Thanks

Answer 1

The statement 'Jaguars are black' is ambiguous, especially given the lack of context. In common language the context will often clarify whether the qualifier 'all' or 'some' should be inferred.

Example: Newborn babies can't walk. ---> ALL newborns can't walk.

Example: Men were involved in a bar fight last night. ---> SOME men were involved in a abr fight last night.

Answer 2

Statements in formal logic without a qualifier are interpreted as universal, and their truth values are usually calculated in the formal system of Prepositional Calculus/Logic. In other words, The statement jaguars are black will assigned the universal qualifier "all".
Since there are counterexamples, the statement is false. If, however , you made the specification of "Some Jaguars are black", it would enter the realm of Predicate Calculus/Logic, and then the truth value would change to true. The interpretation would be "there exists at least one Jaguar that has the property/predicate of blackness". The above would also hold in Categorical/Aristotelian Logic.

Answer 3

Hello,
The statement is false. To say, 'Jaguars are black' is to say, 'If x is a jaguar, then x is black.' However, since 1 in 16 jaguars are black, 15 of those jaguars are not black. So the statement 'if x is a jaguar, then x is black' is false.

Answer 4

In formal logic, the statement is meaningless. Jaguars is a set of animals, and a set is never black.

In formal logic, you'd either state that:

All jaguars are black.

or

Some jaguars are black.

But that's formal logic.

In casual speech, the sentence probably does mean that "all jaguars," but that depends on the context of the sentence. Formal logic is about making sentences clear, and this sentence is not clear.

Answer 5

yes... i agree with you... if you say that jaguars are black, you are not implying that ALL jaguars are black, but people will assume that you mean all jaguars are black. but that's human stupidity right there.

Answer 6

yes the statement is true because jaguars are in deed, black, the fact that not all are of that color could mean the statement is misleading, but not untrue.

Answer 7

i took logic along time ago, and with just one premise as such i believe the second statement is false regardless of whether or not the word ALL is used. i think that it is implied in this case. but, as i said it was a long time ago.