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Imagine that you are a detective and you are investigating a crime. Suppose you can't point to a criminal yet. However, you can name him in your reasoning. You can call him the criminal, the murderer, Mr. X, and so on. So the question is, why can we do that? What does the word criminal mean in this case? Don't we need to know which object the name is pointing to?

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Similar reasoning can be found in mathematics. For example, if you have some predicate P and you know that there is at least one value that satisfies the predicate, then you can denote this value with a letter (for example, n) and use it in further reasoning. For example, if P = "be an even prime number", then n denotes a specific number 2. If P = "be a prime number", then n is not the name of a specific object, but a variable that takes a value on prime numbers. A completely strange situation occurs if we prove the non-existence of an object by contradiction. Then we believe that such an object still exists and denote it by a letter, but in the course of reasoning we come to a contradiction. In this situation, it turns out that n does not mean anything at all. I am interested on what philosophical principles such reasoning is based

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    John Doe.......
    – Mauro ALLEGRANZA
    Apr 5, 2022 at 19:02
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    How can you name someone you can point to? What additional difficulty do you think is caused by the fact that you can't point to someone? Does this difficulty apply to someone you haven't seen but a third party tells you about? Does it apply to historical figures?
    – David Gudeman
    Apr 5, 2022 at 21:55
  • When I name someone I can point to, it seems clear to me. There are 3 objects in this situation: 1. Name 2. Interpreter (person) 3. Object. The interpreter somehow perceives the name and associates it with the object. But when the object is not known, such scheme stops working. Also above, I described some of the problems that arise in this case using the example of mathematical reasoning.
    – Alexander Chaikov
    Apr 6, 2022 at 5:19
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    When you start knowing something? a) even if you shake his hand, you don't know him (knowing somebody is knowing a lot of facts about him) b) you already know him: he's the criminal (knowing somebody is knowing some facts about him).
    – RodolfoAP
    Apr 6, 2022 at 6:39
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    From a logical point of view, see Existential elimination: you assume that an object exists with property P and you call it provisionally c: thus, we have Pc. Then we derive a contradiction and thus we conclude that the initial assumption is false, i.e. we conclude that there is no object with property P. Now the "provisional" name c disappear.
    – Mauro ALLEGRANZA
    Apr 6, 2022 at 10:01

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Well, this unknown entity that has committed the crime is unlikely to be an ashtray, a chair, a cupboard. Or even a knife or a gun. It is, as you have implicitly acknowledged a human being as these are the only beings on this earth that can commit intentional acts.

Hence Mr. X refers to an unknown element of the set of human beings. By this, you already know a vast number of facts about him as we already know a vast number of facts about human beings. We constrain this element as the one who has committed this crime. Variables name elements that range over a set. Mr. X is the name of a variable. Once Mr. X has been identified then we will have identified the criminal.

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We need to know something about the thing we name, but it does not have to be exhaustive. Indeed, if it had to be exhaustive, we could not name things: there is nothing about which we know everything.

For instance, I was able to name something "the thing" even though I knew nothing more about it than it can be named.

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When naming an abstract concept, you simultaneously provide a name for any concrete object that happens to typify/instantiate/resemble it.

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