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Unicorns don't exist, but I can still describe unicorns as "unicorns have four legs".

Does the statement "unicorns have four legs" have no truth-value or is it always false, similar to how Russell says "the king of France is bald" and "the king of France is not bald" are both false?

According to some dictionary, "true" is defined as "in accordance with fact or reality".

Of course, we can say "according to some legend, book, etc, unicorns have four legs", and it's true, but what if I start with "according to reality"?

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  • i upvoted becasue it seems to be what you were getting at with the other similar questions. personally, i believe that it is justified for me to claim that unicorns have horns, at least in some fictional way, so why think it isn't true? do fictional entities have any reality?
    – user67675
    Nov 26, 2023 at 6:57
  • @prof_ghost Of course, they have no reality, but when it comes to fictional entities, according to my intuition, it has no truth-value.
    – user68943
    Nov 26, 2023 at 7:02
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    Does this answer your question? Can we describe round square, which doesn't exist?
    – Conifold
    Nov 26, 2023 at 8:01
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    You know what they say about doing the same thing and expecting a different result? Especially over and over and over again.
    – Conifold
    Nov 26, 2023 at 8:05
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    You should probably figure out the exact thing you actually want an answer to, that would resolve the topic for you. Because you've asked about a dozen questions in the last week or so about the same thing, many/most of which come down to pretty much the same answer.
    – NotThatGuy
    Nov 26, 2023 at 20:33

12 Answers 12

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I think your questions seem to have the common denominator of trying to apply the straitjacket of logic to everyday speech. When we say 'unicorns have four legs' it is an idiomatic shorthand for something along the lines of 'there are well-known fictional ideas of four-legged horses with single horns to which we give the name unicorn'. The long-hand version is true, and the short hand version, idiomatically, is understood to be true as well.

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    +1 "idiomatic shorthand". We also have a term in philosophy: truth-apt.
    – J D
    Nov 26, 2023 at 17:31
  • @JD many thanks indeed for the helpful and supportive comment. You might have gathered that my awareness of technical terms in philosophy is shamefully narrow, so I welcome any and all coaching from wiser members of the site. Expect to see 'truth apt' littered across my future answers! All the best. Nov 26, 2023 at 20:14
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We should interpret "unicorns have four legs" as, "If unicorns were real, they would have four legs." This is an example of a counterfactual conditional; it says what would follow, if circumstances were hypothetically set up to be a certain way, whether or not they really are that way in reality.

It is a true statement; if an animal existed with the properties of a unicorn, that animal would have four legs.

Other examples of how counterfactuals can be used to interpret statements:

  • Harry Potter is a student at Hogwarts. (translation: "If Harry Potter existed as described in the books, he would be a student at Hogwarts.")
  • The sum of internal angles of a triangle is 180 degrees. (translation: "If a perfect triangle existed as described in Euclidean geometry, it would have a sum of internal angles equal to 180 degrees.")
  • The cloak is soft. (translation: "If you touched the cloak, you would experience a sensation of softness.")

That last one shows that even statements about physical reality are often really about what would happen under counterfactual circumstances. An object's properties are determined by how the object would interact with other objects, whether or not it is currently doing so.

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  • Then, if it doesn't exist, does the sentence have no truth-value?
    – user68943
    Nov 26, 2023 at 8:09
  • @Collins As I said, it has a truth-value of "true." Counterfactuals allow us to make true statements about what would happen under certain circumstances, even when those circumstances are not currently the case.
    – causative
    Nov 26, 2023 at 8:13
  • How would you describe this if it were not known if the assumption were true? We know Harry Potter is not real (the assumption is not true, Harry Potter is not real), but we can reason about it as if it were. ... What if the question is "If P=NP then X=Y"? We do not know if P=NP, but we can reason about it. What then?
    – Ben
    Nov 26, 2023 at 18:57
  • @Ben Contrast typed set theory with ZFC: it's perfectly possible to talk about reasoning in various logical systems without relating those internal notions of "truth" to real-world truth (if you believe in a privileged real-world truth). (See also: the object language / meta language distinction.)
    – wizzwizz4
    Nov 26, 2023 at 23:34
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    @Ben That's still just a "counterfactual conditional," whether or not B is false. The SEP article explains this. You could also call it a "subjunctive conditional" or a "hypothetical conditional," but "counterfactual" is the more usual term, if a bit misleading.
    – causative
    Nov 28, 2023 at 19:55
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  1. If one distiguishes between a concept and it referent, then the concept “unicorn” does not have a referent. Also the concept of a “unicorn with four legs” does not have a referent. Hence the sentence “unicorns have four legs” has no meaning. As a consequence it does not have a truth value.

    Speaking about unicorns is always speaking about the concept “unicorn”.

  2. Could you please give a precise reference where Russell makes the above claim. Ascribing the truth value “false” to the statement “the king of France is bald” implies that the opposite statement “the king of France is not bald” is a true statement, which seems equally meaningless.

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  • It's the edited part, I wrote only that "the king of France is bald" is false according to Russell.
    – user68943
    Nov 26, 2023 at 7:13
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    Can I ask something? is "unicorns have four legs" also a concept?
    – user68943
    Nov 26, 2023 at 7:54
  • @Collins No, I consider this a sentence, but a meaningless one.
    – Jo Wehler
    Nov 26, 2023 at 7:57
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    Do you think "an unicorn doesn't exist" is also meaningless because the concept "unicorn" doesn't have a referent?
    – user68943
    Nov 26, 2023 at 8:29
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    @Collins IMO the sentence “an unicorn doesn't exists” is a problematic sentence. But it is clear what the sentence intends to say. In order to avoid pseudo problems due to the misuse of language, it is better to explicitly distinguish concept and referent. And to say “The concept 'unicorn' has no referent”.
    – Jo Wehler
    Nov 26, 2023 at 8:50
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Is to be able to describe something to be able to judge that it's true or not?

No. The best example I can give is the myth of the cyclops and ancient elephant bones. The bones of ancient dwarf elephants or mastadons can be arranged to look like a tall human with one huge eye (trunk). So early Greeks discovering these bones described it and judge it to be real (Cyclops) but were wrong.

Cyclops Myth Spurred by 'One-Eyed' Fossils? - National Geographic https://www.nationalgeographic.com/science/article/news-deinotherium-fossils-crete-mythology-paleontology

https://www.forbes.com/sites/kristinakillgrove/2017/09/26/can-a-human-cyclops-exist-historians-paleontologists-and-ancient-aliens-weigh-in/

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You ask:

Does the statement "unicorns have four legs" have no truth-value or is it always false

The modern solution for dealing with unicorns is to simply label them philosophically as fictions. From WP:

Fictionalism is the view in philosophy according to which statements that appear to be descriptions of the world should not be construed as such, but should instead be understood as cases of "make believe", of pretending to treat something as literally true (a "useful fiction").

This is related to the notion there are different contexts or domains of discourse which are in some sense independent of each other. Thus, "unicorns have four legs" is true relative to the domain of discourse. Certainly, if one is talking about Lord of the Rings and the Middle-Earth, it is a true sentence. If the domain of discourse is the tree of life on physical earth, our earth, then claims about fictional organisms are either false or meaningless even if they are well-formed.

One might press the question, is it true or not, then, in which case philosophers have invented the term truth-apt (oxfordreference.com):

A sentence is truth apt if there is some context in which it could be uttered (with its present meaning) and express a true or false proposition.

Thus, to argue anymore over whether the sentence is true is merely resolved by accepting that it is true within a domain of discourse, that is, the sentence is truth-apt.

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  • It's an alternative truth.
    – Scott Rowe
    Dec 6, 2023 at 16:00
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    @ScottRowe And alternative truths are the basis of alternative facts. :D
    – J D
    Dec 6, 2023 at 17:05
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Is to be able to describe something to be able to judge that it's true or not?

Of course, we can say "according to some legend, book, etc, unicorns have four legs", and it's true, but what if I start with "according to reality"?

Let's say, for the sake of argument, that human brains and human minds are objectively real. Then we could say that some concept of "unicorn" objectively exists as information represented in the connections between neurons of the physical brains of most humans (excluding of course those humans who have never being exposed to the concept). Then, it is objectively true according to reality that most human brains would logically conclude that the statement "unicorns have four legs" is consistent with the concept of "unicorn" they had previously learned. This is grounded in the information processing capabilities of biological human brains, which we already conceded are real. We can empirically verify this by testing it with many humans (ask each person on the planet for a definition of "unicorn" and then ask them whether a unicorn has four legs, and record the responses). We can also extend this to artificial systems, such as Large Language Models like ChatGPT, that also have the capacity to represent concepts and then perform logical inferences over them. Again, all this is objectively grounded in real physical systems (brains, computers, etc.) that are capable of representing and storing concepts and reasoning over them.

In other words, I'm suggesting that your question "is it true that unicorns have four legs according to reality?" should be rephrased as "Is it objectively true that if a human brain or a computer with similar reasoning capabilities learns the concept of 'unicorn', it would conclude that the statement 'unicorns have four legs' is logically entailed by the definition of the concept?", the answer to which would be "in most cases, yes, with the exception of information processing systems (brains, computers, etc.) with their cognitive faculties impaired in a way that would prevent them from performing a valid logical inference".

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Concepts can be real or imaginary. “Unicorns have four legs” is a true statement within a context. All true or false statements have context of real or imaginary. Here it is the imaginary Unicorn. Given the imaginary Unicorn , is it true the Unicorn have four legs? The answer is Yes.

One should be careful while answering questions or making statements.

Suppose you don’t own a private company, then if I ask you : Have you stopped running your company? The answer is not yes or no. The answer is ,you don’t own any company.

Similarly “King of France is bald” can be true or false only if king of France exists for real or in imagination.

There are paradoxical statements as well. For example - “I always lie.”

Some statements can not be understood unless felt. For example -“ Consciousness is infinite” ,Or ,”There is a rib-cage breaking pain.” Such statements are real but their significance can not be understood unless felt. Their truth value is little known or unknown.

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    You need to include paradoxical statements.
    – Meanach
    Nov 26, 2023 at 11:17
  • @Meanach Yes. There are paradoxical statements as well. For example - I always lie. Nov 26, 2023 at 12:36
  • Good to know. But it was an editorial suggestion.
    – Meanach
    Nov 26, 2023 at 12:42
  • For example, is Picasso a madman that everyone agrees on? You should discover the power of image processing. And you can check out DALL-E if you are not busy.
    – fkybrd
    Nov 26, 2023 at 16:45
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Is to be able to describe something to be able to judge that it's true or not?

Clearly not. Every single scientific proposition is by nature "falsifiable" (or else it is not a scientific statement). Every one of them has to be an exact description of "something", or else we wouldn't know what to falsify.

And very clearly, not everyone of them is true - that is the very meaning of "falsifiable".

Some proposals have taken decades or centuries to solve, i.e. to find out whether they are true or not (e.g., Descartes' Theorem).

So yes, we can describe something (a scientific theory or theorem), and it can very much not be true, and often we do not know beforehand.

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Orange horses have four legs. However, I have no idea if any orange horses exist.

Now I say “all unicorns have six legs” and “all orange horses have six legs”. I’m quite sure the first statement is true, but again no idea whether the second one is true, but I e we wouldn’t bet on it.

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According to reality

are fictions sometimes true, always false, or do they have no truth value? Fictional entiies are not real, and do not exist in reality, so you can go with e.g. Russell (false) or e.g. Strawson (neither true nor false), but you probably cannot say they are ever true about reality, certainly not if by 'reality' we mean what exists independent of our fictions.

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You say :

but what if I start with "according to reality"?

Reality becomes objective at the moment of interaction. Until then, it's just a potential. Every interaction happens inside a context. In your case it's that "according to some legend, book, etc" that is the context.

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  • ie. If I don't listen to my mother telling me not to burn your house down and instead listen to the voices in my head telling me to burn your house down, then the voices in my head are objectively more real to you than my mother is.
    – DKNguyen
    Nov 26, 2023 at 23:34
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"Unicorns have four legs" is just as true as "Harry Potter is a wizard" and "Captain Kirk was (or will be) born in Iowa."

These are all fictional beings, so when we talk about them it's from the perspective of the world in which they're imagined to exist.

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