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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?

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    $\begingroup$ I agree with Roy, your statement is just false if you include as true the fact that "yuo do not own any car". No further impications. $\endgroup$ – Wolphram jonny Jul 15 '14 at 10:06
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    $\begingroup$ Of course "my" need not imply ownership. People say "Driver, please hurry, I have to catch my plane" instead of "the plane for which I have purchased a ticket". $\endgroup$ – Hagen von Eitzen Jul 15 '14 at 10:12
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    $\begingroup$ Given the expression "If I have a car, then there is a dead body in it" and the statement "I don't have a car", the former is true due to the fact that false implies anything. Your question, however, is not phrased in a similar manner, which would allow us to derive the same logical conclusion. $\endgroup$ – barak manos Jul 15 '14 at 14:50
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    $\begingroup$ This seems to be more a question about the English language than about mathematical logic. $\endgroup$ – Peter Taylor Jul 16 '14 at 11:02
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    $\begingroup$ i am quite disappointed that some people consider this an offtopic question. this in no way was supposed to be a question related to english language at all. the original question we discussed with a friend was not spoken in an english language at all. it is the commentators who turned this question into speculations related to the ambiguities of english language. this is question related to logic in every sense of the word. and there are two ways to understand this logical statement that english language allows us to. definitely not a question about english language. disagree about of-topic $\endgroup$ – user151496 Jul 16 '14 at 13:50

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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.

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    $\begingroup$ I do not agree that it is a case of definite description; the original Russell's proposal was related to "The F is G", treated as "∃x(Fx & ∀y(Fy → x=y) & Gx)". If we apply it to "my car" we have that "∃x(car(x) & ∀y(car(y) → x=y) & my(x))" meaning that there is only one car in the world and it is mine. $\endgroup$ – Mauro ALLEGRANZA Jul 15 '14 at 15:27
  • $\begingroup$ @MauroALLEGRANZA: Isn't it an improper definite description (by Wikipedia's definition)? $\endgroup$ – Roy O. Jul 15 '14 at 15:34
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    $\begingroup$ I think so; according to Theory of descriptions the indefinite description "some dog is annoying" must be formalized as $∃x(Dx \land Ax)$. THus we can translate the OP's original sentence as $\exists x \exists y[Body(x) \land Car(y) \land Owner(I,y) \land Ontop(x,y)]$. $\endgroup$ – Mauro ALLEGRANZA Jul 15 '14 at 15:45
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    $\begingroup$ @MauroALLEGRANZA: I was too sloppy yesterday and I now agree that it was incorrect. Because my answer is accepted I apparently cannot delete it (which seems appropriate due to the substantial change in content), but I think the answer is at least correct now. Thank you. $\endgroup$ – Roy O. Jul 16 '14 at 12:17
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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.

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

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  • $\begingroup$ thanks for the answer; however, isn't it also "definite description", as Roy O. said? $\endgroup$ – user151496 Jul 15 '14 at 13:14
  • $\begingroup$ No, it isn't. because 'each of my cars' does not imply any such car exists. And if there's no such car then 'my cars' denotes an empty set of cars, so the whole statement becomes true. Same way - if we assume vampires do not exist - the sentence 'every vampire drinks blood' remains true. $\endgroup$ – CiaPan Jul 15 '14 at 14:19
  • $\begingroup$ It is still a definite description, but of the set, not a single car. $\endgroup$ – nmclean Jul 15 '14 at 15:01
  • $\begingroup$ However language is a very ambiguous thing; if I (equivalently?) rephrase my sentence as "I have found dead bodies on my cars, one body on each of them", then I am no longer sure it remains true... $\endgroup$ – Vladimir Jul 16 '14 at 9:23
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    $\begingroup$ Anyway, the question and the subsequent discussion reminds me of the following anecdote. A professor of linguistics gives a lecture. He says, "There are many languages in which double negation is still a negation. There are many languages in which double negation means affirmation. But there are no languages where double affirmation counts as negation." A student replies, sarcastically, "Oh yes, of course." (Sorry for possible off-topic.) $\endgroup$ – Vladimir Jul 16 '14 at 9:46
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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 .

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  • $\begingroup$ sorry, Roy's answer appeared again! $\endgroup$ – Wolphram jonny Jul 15 '14 at 10:12
  • $\begingroup$ My mistake. I thought of writing an extended answer, but I then considered it sufficient. :) $\endgroup$ – Roy O. Jul 15 '14 at 10:22
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The statement could be true or false.

You HAVE found a dead body on MY car

implies you found it in the past. The fact that you do not own a car only implies to be true NOW.

So without more information we can not presume anything. My next question would be "Have you ever owned a car?" and then "When did you find the body?".

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    $\begingroup$ Saves me from adding my own answer. The past tense opens it up. $\endgroup$ – user2338816 Jul 16 '14 at 5:01
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I would take a different approach and say you can not determine if this statement is false or true by the information provided.
While you do not OWN a car, you could have a rental car (so not owned) but still would qualify as being "my car".

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In English "my car" can mean any car you are currently using, whether it be borrowed, rented, stolen, or a chauffeured vehicle like a taxi or limousine. Moreover, "car" can also mean "truck" or "SUV" etc. Therefore we cannot determine if the statement is false just because we are told that you "do not own any car"; although the word "any" would strongly imply that trucks and SUVs are off the plate, cars you don't own can still be "your car" in many contexts.

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I think the statement that acts the way you are thinking is the statement "If I have a car, then I found a dead body on it." This statement is a case of false implies anything is true.

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Is true the statement?.

Answer:

STATEMENT equals CAR implies FOUND-DEADBODY

If you own a car then you found a dead body, hence it is true even if you don't own a car

or you could say

STATEMENT equals FOUND-DEADBODY and OWN-A-CAR

However, you found a dead body only if you own a car and since you don't own one then, the statement is false

I.e. the solution is how you interpret the statement.

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"considering the fact that I do not own any car" is a red herring -- people use the phrase "my car" or "my house" all the time and none of them require actual ownership.

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