"I have found a dead body on my car."

Given a statement "I have found a dead body on my car", and considering the fact that I do not own any car, is this statement true?

If so, is this a special case of false implies anything?

Solution 1:

Ignoring matters of ambiguity in natural language (since this does not seem relevant to what you are asking), your sentence could be rephrased as:

$$\text{'I have found a dead body on a car that I own'}$$

where 'a car that I own' is an indefinite description according to Russell's theory of descriptions. The whole sentence may be formalised as follows:

$$\exists x,y : \mathrm{car}(x) \wedge \mathrm{body}(y) \wedge \mathrm{dead}(y) \wedge \mathrm{foundOnTopOf}(i,y,x) \wedge \mathrm{owns}(i,x)$$

If you don't own a car, then the statement is false, since you are in part asserting that there exists a car that is yours.

Solution 2:

There is no implication in your statement. A natural translation into first-order logic would be something like "There exist a car and a person such that: the car is mine and the person is dead and the person is on top of the car."

If you do not own a car, then the statement is false since "the car is mine" is always false.

Solution 3:

If you do not own any cars, the following statement will be true: "I have found a dead body on each of my cars."

Solution 4:

Well, Roy seemed to disappear, so I'll add my comment as an answer: Your statement is just false if you include as true the fact that "you do not own any car". No further implications seem important .