I am asking this question because I thought what truth value would have a have a quantifier over a set that contains persons that are dead. For example suppose I state:

"For every x that is member of the 1850 goverment of France, x is playing football right now".

It is clear that all members of the 1850 France are now dead. So this is equivalent to asking if we make statements about persons that are dead. So lets assume John is one of these members. Then the statement:

"John is playing football right now". Is it true or false? I was thinking about using Russel's definite description theory but what bothers me is if his theory applies only for person/objects that have never existed.

Edit After reading the comments I think I should add some details. As I said the problem boils down to the individual statements of the quantifier (at the end of the day the conjuction of these statement will determine if the whole statement is true or false). Leaving aside "John" for the moment I thought the following sentence.

The airplane that Mr. X used in 1989 is now above New York.

We know that this airplane was destroyed in 1990. By reading the comments I understood that we can give a truth value because the "existence" can be viewed transtemporally. And that makes sense because I can give a truth value also for the statement:

The airplane that Mr.X used in 1989 was destroyed in 1992.

I thought to model objects/persons that have been existed as "functions" where before their creation/birth (I apologize if there is a technical term) and after their destruction/death have the value zero and non-zero everywhere else. Then by applying an operator to that function we can get back a value. The operator is the question e.g.:

Is the airplane that Mr. X used in 1989 is now above New York?

and the action of the operator will return back a value (T or F). Does it make any sense? I searched about "modal predicate logic with varying domains" but I don't have the theoretical background.

  • 1
    You may be interested in modal predicate logic with varying domains. – lemontree Nov 28 '20 at 12:08
  • 1
    Russel's paraphrase can be easily combined with tenses. In your case, the paraphrase will be "There exists John, who was a member of the 1850 government of France and is playing football right now". It is false. "Exists" here is interpreted transtemporally, "exists/ed somewhere in spacetime". – Conifold Nov 28 '20 at 13:01
  • U can try free logic or temporal logic. – Double Knot Jun 10 at 1:23

Regarding your first proposition:

For every x that is member of the 1850 government of France, x is playing football right now

If your quantification domain of discourse D is all current living people then clearly it's false after paraphrasing above into a conjunctional well-formed formula of FOL even the description "member of the 1850 government of France" is not definite at all.

Now regarding your next question:

So lets assume John is one of these members. Then the statement: "John is playing football right now". Is it true or false?

Intuitively it should be still false but as you rightly conceived it cannot be expressed in classic FOL since your supposed John is outside your above defined D, and worse John is a proper name not a definite description. This is the case where a weaker form of classic FOL called free logic comes to help if you don't have to unnecessarily paraphrase John into a definite description just to get around this technical issue. As the SEP reference mentioned:

classical logic is unreliable in application to statements containing singular terms whose referents either do not exist or are not known to. Consider, for example, the true statement: (S) We detect no motion of the earth relative to the ether, using ‘the ether’ as a singular term for the light-bearing medium posited by nineteenth century physicists. The reason why (S) is true is that, as we now know, the ether does not exist. According to classical logic, however, (S) is false, because it implies the existence of the ether. Free logic allows such statements to be true despite the non-referring singular term.

To distinguish terms that denote members of D from those that do not, free logic often employs the one-place “existence” predicate, E!. For any singular term t, E!t is true if t denotes a member of D, false otherwise.

So now you can express above in free logic as Pj ∧ E!j with the same D defined above.

Finally for your remaining examples with tense, it's better to use first order temporal logic (FOTL) to express such as the truth value of Aristotle's proposition "there will be a sea battle tomorrow". As the SEP reference mentioned:

the varying domain semantics can be simulated in the constant domain semantics by adding to the language of FOTL an existence predicate for ‘existence at the current time instant’, which can be defined in the varying domain semantics by E(τ):=∃x(x=τ)... To generalize, for every formula φ of FOTL, its E-relativization in the extended language can be obtained by replacing every occurrence of ∀x in φ by “∀x(Ex→...)” and every occurence of ∃x by “∃x(Ex∧...)”... The question that remains, from a philosophical point of view, is whether existence is a legitimate predicate. An axiomatic system for the minimal FOTL with existence predicate can be obtained along the lines of free logic...

The models of FOTL are based on temporal frames where each time instant is associated with a first-order relational structure. Formally, a first-order temporal model is a quintuple: M=(T,≺,U,D,I)

So the easiest way out in FOTL is to adopt eternalism's constant domain POV to express your tensed proposition "The airplane that Mr. X used in 1989 is now above New York." as ∃p(Ep ∧ Xp ∧ Np)) with global domain U and local domain D defined and interpreted by your model.

  • Over the set of living people, X was a member of the French government in 1850 is false in all cases. Hence, any conditional is true since the antecedent is false. Over the set of people (living and dead), the statement is false. (Most immortal human-looking beings in literature count either as not people or not living.) – David Thornley Jun 10 at 21:35
  • @DavidThornley thx for your comment. For " X was a member of the French government in 1850" I only see it's a part of conjunction with "X is playing football" as another part. I don't think they're material implication relations though... – Double Knot Jun 10 at 21:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.