For: I can be thinking about Frodo. I can think, e.g. that Frodo was the character introduced in the second chapter of LOTR, or that Smeagol was the hobbit who fell to his doom at the end of the book. I can think that Frodo was a Christ-like character. So we can think about fictional characters.

Against: ‘aRb’ implies ‘for some x, aRx’. So if ‘I am thinking about Frodo’ is true, then so is ‘some x, namely Frodo, is such that I am thinking about x’. But there is no such thing as Frodo, and there never was. So we cannot think about fictional characters. [edit] This is even true of ideas about fictional characters. 'Tom has an idea about Frodo' is also of the form 'aRb', where R = 'has an idea about', and so is 'Tom is thinking about his idea of Frodo'. Therefore we cannot have ideas about fictional characters, nor can we even think about ideas of them.


3 Answers 3


This problem is only illusory.

In paragraph 1, you are talking about the ability to have an idea.

In paragraph 2, you are referring to whether that thought has a referent in the real world.

The resolution: the thought exists in your head and is real regardless of whether the thought has a referent or not. Basic reason is that thoughts belong to thinkers. Existence in the world is something else.

  • "In paragraph 1, you are talking about the ability to have an idea. " Yes, but the ability to have an idea about Frodo. I am not thinking about the idea of Frodo, rather I am thinking about Frodo. Similarly the name 'Frodo' refers to Frodo, whereas 'my idea of Frodo' refers to my idea of Frodo. The idea of Frodo, and Frodo, are separate things. Jul 4, 2014 at 16:31
  • @quisestille No, in fact, you are thinking about your idea of Frodo or you are thinking about a common social idea of Frodo -- say one that arrives from reading a book or wathing a movie. In that respect, the idea is real even if it has no physical referent that is a hobbit.
    – virmaior
    Jul 4, 2014 at 16:34
  • See my edit above. You can't even think about your idea of Frodo. Jul 4, 2014 at 17:57
  • 1
    @quisestille - Of course you can. You're just selecting the wrong universe U to pick x from in "for some x". Otherwise you couldn't think about Abraham Lincoln (no Abe any more, the referent is gone!) or even your best friend (since you have no access to them, only to your concepts of what that friend is like, and those only from past interactions).
    – Rex Kerr
    Jul 4, 2014 at 18:43
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    @quisestille - I am saying that x is drawn from a set of thinkable-about-things. You can think about things that do not exist, like an abstract symbol x, the number zero, Rapunzel, Darth Vader, an invisible pink unicorn, and so on.
    – Rex Kerr
    Jul 4, 2014 at 23:17

aRb implies "for some x in the set of referrable-to's, aRx". It doesn't mean x is an extant physical entity unless that is implicit in R.

For example, 3 < 4 doesn't tell you that there's a physical entity to which you're referring. Rather, it's a relation on natural numbers, none of which are extant physical entities.

As another example, Superman is taller than Lois Lane doesn't mean there's an extant Superman or Lois Lane, just that there is some collection of propositions involving the reference "Superman", and "Lois Lane", and that you can deduce from those that Superman is taller.

There is some difference between thinking about actual objects and pretend ones, but it's cognitively subtle. You're doing all the same stuff: recalling facts, checking them for accuracy and consistency, performing deductions, maybe even querying the physical world for evidence (reading Lord of the Rings, for example). You don't get Abraham Lincoln imported directly into your consciousness either; you read about him. You don't get Justin Timberlake imported directly into your consciousness either.

Saying that you are not "thinking about" stuff just because it happens to not exist, when it doesn't matter at all to what you're doing whether it exists or not, is a poor choice for terminology. If you say "I am thinking about Frodo" but your thoughts don't conform very well to what Tolkien wrote, then I could argue that you are not thinking about Frodo, but then again if you're thinking about "Abe Lincoln" but he's actually a vampire-slayer not a President, I again might say you're not; and if you are thinking about Justin Timberlake, astronaut and expert skiier, well, again, I can argue that you're not actually thinking about the canonical Justin Timberlake.

So, in summary: a name need not refer to an existing person, just something that can be reasonably unambiguously identified and has a set of associated propositions that are true or false about it. Defining "thinking about" to mean something else pointlessly complicates communication.


This is a well-known problem in the philosophy of language and it is well-known that there is no simple answer. Neither of the two answers above even alluded to this fact. There are two answers commonly given, both of which are flawed. The first is that 'Tom is thinking of N' really means 'Tom is thinking of his idea of N'. The standard reply is that if we want to talk about an idea of a thing rather than the thing itself, we use expressions like "Tom's idea of N" rather than 'N'. Frege ("On Sense and Reference") says "When we say 'the Moon', we do not intend to speak of our idea of the Moon, nor are we satisfied with the sense alone, but we presuppose a reference. To assume that in the sentence 'The Moon is smaller than the Earth' the idea of the Moon is in question, would be flatly to misunderstand the sense. If this is what the speaker wanted, he would use the phrase 'my idea of the Moon'". I alluded to this above. I also added another argument. Let's grant that 'Tom is thinking of N' really means 'Tom is thinking of his idea of N'. But then you still have the same problem: 'Tom is thinking of his idea of N' also has the form aRb, and so logically implies that for some x, aRx, i.e. that for some x, Tom is thinking of his idea of x. If you try to avoid this by the same manoeuvre, you get trapped in an infinite regress.

Alongside this, it's very common to bring psychology into the question. E.g. Rex above says "There is some difference between thinking about actual objects and pretend ones, but it's cognitively subtle." But this is a logical problem, not a psychological problem. "Tom is thinking of Frodo" appears to have the logical from 'aRb', and in standard logic, aRb implies for some x, aRx. Any satisfactory answer either needs to take this on board, or to reject standard logic.

The second answer commonly given is that 'Ex aRx' follows, but 'x' ranges over all sorts of non-standard objects, such as 'non extant objects', whatever that means. Rex gives the example of the true proposition '3 < 4'. This implies that something is less then 4 (namely the number 3), even though the number 3 is not a physical or concrete object, but an abstract object. That's broadly correct, but doesn't answer the question. The problem was 'Tom is thinking of Frodo' in standard logic implies there is such a thing as Frodo. However, the second horn of the dilemma is that there is no such thing as Frodo. This is not analogous to the case of '3 < 4'. For there is such a thing as the number 3, and the number 4. But there isn't such a thing as Frodo.

So both of the well-known replies above are wrong, and it is also well-known that they are wrong.

Another standard reply are that 'Tom is thinking of Frodo' is false, yet another is that it is meaningless, since no proposition with a fictional name in it can have a truth value

My own answer to the question is simply that 'Tom is thinking of Frodo' doesn't imply that there is such a thing as Frodo, and so is consistent with 'there is no such thing as Frodo'. This means that we can't interpret it as having the logical form 'aRb'.

  • I think you're overreading my answer to thoroughly associate it with something else. Moreover, I don't see any difference whatsoever between my answer and your last paragraph. You're misunderstanding the idea of X move or at least missing what I am saying. My answer is not that you are thinking of your idea of X it is that what you have is {your thought of X} -- which may or may not have a real world referent. Some thoughts like unicorns or frodo have long stories to explain what they refer to that you think of. Others like the water glass in front of me don't... both are thoughts of thinkers.
    – virmaior
    Jul 5, 2014 at 8:43
  • As with the original reference problem you're referring to, the problem is actually illusory and depends on an artificial separation -- as I suggested in my answer.
    – virmaior
    Jul 5, 2014 at 8:43
  • You said in your comment a while ago: “you are thinking about your idea of Frodo or you are thinking about a common social idea of Frodo”. But now you say “My answer is not that you are thinking of your idea of X”. Which is it? Jul 5, 2014 at 9:20
  • It's both. There's nothing incongruous in the two answers as I've used them.
    – virmaior
    Jul 5, 2014 at 9:29
  • So it's both? i.e your answer is that I am thinking about my idea of Frodo and your answer is NOT that I am thinking about my idea of Frodo. Doesn't the word 'not' signify contradiction? Jul 5, 2014 at 9:34

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