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Suppose a person makes a statement such as, "I have 9 toes." Yet this person has never lost a toe.

The statement is true in that the person does have 9 toes. But it's also more accurately true that this person has 10 toes. Does that make the statement a lie? A half truth? That seems too generous. How do you classify a statement like this?

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    It is an imprecise statement; see Fuzzy Logic. – Mauro ALLEGRANZA Oct 23 '17 at 15:13
  • Nice -- Imprecise statement. I like that, thank you. Good link too, though a lot of it is way over my head. :) – I0_ol Oct 23 '17 at 19:38
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    There is a difference between vague, ambiguous, and inspecific statements. If this one is meant as "I have at least 9 toes" then it is inspecific but entirely true, and if it is meant as "I have 9 toes exactly" then it is entirely false. As is, it is ambiguous, but not "not entirely true and not entirely false". The latter description, and fuzzy logic, only apply to vague statements, such as "30 grains are a heap". – Conifold Oct 23 '17 at 20:58
  • It might be more interesting to examine Heraclitus' statement 'We are and are-not', which he proposes is true. Or, for a similar case, 'an electron is not a wave or a particle'. Where a double-aspect theory is involved such statements become possible. They are rigorous but not strictly true or false without further information and clarification. . – PeterJ Nov 23 '17 at 12:49
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The statement "I have 9 toes" is true because they have 9 toes. If they then said "I have 10 toes", that would also be true, because they have 10 toes.

Note that I am assuming that "having a toe" means that the toe is attached to the person's body, and that I am also assuming that the person has 10 toes attached to their body. You said that the person "never lost a toe", but this point is completely irrelevant to the question because you didn't say how many toes they were born with. Were they born with 9 toes?

I met a super-hot Japanese girl from Hiroshima who has 10 toes. She was born with 12 "foot fingers" (as she called them), but her parents gave a doctor permission to cut 2 off soon after she was born.

Someone else said that "I have 9 toes" is an "imprecise statement". I agree that it is an imprecise statement, but not because the person only told you about 9 of their 10 toes.

"I have 9 toes" is an imprecise statement because the word "have" is ambiguous. Does the person "have" 9 toes attached to their body? Or do they "have" 9 toes in their fridge? etc

"I have 10 toes" is also an imprecise statement for the same reason. So since they are both "imprecise statements", this does not distinguish them and is somewhat irrelevant to the question. It does give some interesting information which is loosely related to the question, but it clearly does not clarify your confusion. I'm only mentioning it to undo the harm done by the person who said it.

Regardless of all of this jabber, the statement "I have 9 toes" is true, and the statement "I have 10 toes" would also be true, and the statement "I have 11 toes" would be false.

A statement can never be "partially" true/false. If your interpretation of the statement is unclear (which seems to be the case here), then either the terms have not clearly been defined, or you do not understand the terms.

When we see an unclear statement, we often try to make assumptions. For your question, I think most people would make the assumptions that I made: that the person has 10 toes attached to their body etc. After making assumptions about the unclear parts, the statement can only ever be either true or false.

In cases where the statement is unclear but no assumption can be made, there can be no "statement" in your mind for you to consider whether it is true or false. For example the statement "it is red", you don't know what I mean by "it", so you can't determine whether it is a true or false statement. But this does not mean the statement is not either true/false. You are only unable to determine whether it is true or false because you don't have enough information, and you can't make assumptions about unclear terms.

Note that we make many assumptions that we may not even be aware about. Your question appears to be more of a "riddle" than a question, but I am assuming it is a legitimate question and not some kind of wordplay.

  • Very nice, spot on. – I0_ol Jan 28 '18 at 4:34
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That statement should be viewed from two sides--from the speaker's side and from the listener's side.

If the person who does not know about numbers well, it is a False statement. Not a lie.

But if he says so deliberately as if he is speaking the truth (denying other possibilities), it is a lie (from the speaker's side) since he is hiding the truth for some other purpose. But from the listener's side it is a doubtful statement. For convention we usually call it a half truth. But I would call it a Partial truth. Otherwise if he says "I have one toe", we will have to treat it also as half truth though the truth in it is almost no.

So, we cannot classify all statements always simply by reading the written form.

The confusion here was because we know the truth already. Or can say, we are already aware of the possibility. Some people tell/write lies to cheat others (e.g. in affidavits; as false statements). You can understand this if you replace 'toe' with 'dollar'. In some occasions we would be compelled to say "That statement is a lie"". We never treat them as imprecise statements after the truth was discovered.

So, the listener's knowledge about the truth also has a great importance in deciding a statement like this.

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The answer belongs, I think, to the pragmatics rather than the semantics of language. If semantics are tied to truth-conditions then 'I have nine toes' is true if and only if I have nine toes. That I also have eight or ten toes is irrelevant to the truth-conditions of the statement.

Pragmatically, though, if we use a notion such as Paul Grice's 'cooperative principle' then the statement, while true, violates the maxim of informativeness (P. Grice, 'Studies in the Way of Words', Cambridge, 1989, 26-7) :

'Make your contribution as informative as is required (for the current purposes of the exchange).

If someone asks me how many fingers I have - I have ten - it is true to say that I have nine because I could not have ten unless I had nine. But this answer violates the cooperativeness principle because my questioner, assuming a standard context, wants to know how many fingers I have in total. By violating the maxim of informativeness I have implied (but not stated) a falsehood. I have not said that I have only nine fingers but this is what, by the cooperativeness principle, I have tacitly implied.

So I should say that 'I have nine toes' states a truth (semantically) but implies a falsehood (pragmatically). Tentatively this, rather than 'not entirely true, not entirely false', is the language I should prefer. It points more clearly, so it seems to me, to what is wrong with the statement in standard contexts.

  • @I0_ol. You have a new answer to your 'nine toes' question. – Geoffrey Thomas Jan 29 '18 at 16:41
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The proposition is either true or false regardless of your emotions. The claim is very specific " I have 9 toes" and is true only when there are exactly 9 toes in total. If the person has less than 9 toes the claim is false. If the person has greater than 9 toes the claim is false. Your assumed proposition in your head appears to be "all humans are born with ten toes" is also false.

I want to advance on my response. Deductive logic involves limiting alternative solutions to two alternatives: true or false and no posible third or greater alternatives. In this way we can rule out a chioce and be certain of the conclusion.

So the literal reading is possible here because the details are super specific. To mean something less than 9 toes should be indicated and not left for the reader to assume.
I chose the literal context because the statement is specific. The less than speicific contexts have worse outcomes.

To say atleast 9 toes as a minimum would indicate a particular quantifier logically. This example is a singular proposition which by rule should be read as a universal. So i would say formally you cant read it as a minimum requirement and still be formally correct. To still apply the minimum context would be at least considered deceptive.

The choice of down playing what you really have is also deceptive practice. For instance if an employer application asks about committed felonies and i reply 2 and then tbe employer discovers i really had 9 would he not think of my claim as intensionally lying? This is why there ought to be rules on how propositions should be formulated. In syllogistic form proposions should be as descriptive as possible. This was hinted by my teachers that using concrete nouns or noun clauses as subjects and predicates minimizes vague terms. That means you cant end a propositional clause with adjectives or adverbs. This way it is harder for the user to swap contexts like some people do with this sample. It is not good that there are individuals that think they can formulate premises any kind of way and be serious about those claims at the same time. Syllogistic rules like what i expressed prevent deceptive pracrices in formal reasoning. This deception prevention is missing in mathematical logic.

The context of the inital argument not taken in the literal sense when the claim is specific leads to a formal argument where the user or creator of such an argument form offers the high possibility of intensional deceptive propositions. I also suggest the reason for Aristotle to formalize arguments was to distinguish deceptive arguments of sophist from arguments done better by philosophers. Yes there is a difference sophists and philosophers. The way philosophers argue is different even if the sophists imitates the philosopher.

  • Sure, the assumption that all people are born with 10 toes is false. But it can be assumed that most people are born with 10 toes. Though I never made the statement all people are born with 10 toes. You seem to be making assumptions about my assumptions ;) – I0_ol Oct 23 '17 at 19:34
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    It's worth pointing out here that there is some disagreement, in the literature on the semantics of count expressions, about the truth conditions of sentences with the form "there are n Fs". Some philosophers think that "there are n Fs" is true just in case there are exactly n Fs; others think that it's true just in case there are at least n Fs. So the claim that "I have 9 toes" is true iff you have exactly 9 toes isn't exactly philosophical common ground. – possibleWorld Oct 23 '17 at 22:19
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    I would say it is true that I have nine toes. (One went to market, one stayed at home...) I'd read it as 'I have at least nine toes'. – PeterJ Oct 24 '17 at 11:51
  • I think if you want to give this answer, you need to explain that the simple logic we teach is often binary and forces T/F and that you contrary to PeterJ and the detail possibleWorld mentions think "I have 9 toes" = "I have exactly 9 toes -- no more and no less" – virmaior Oct 24 '17 at 22:31
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"All statements are true in some sense, false in some sense, meaningless in some sense" - Principia Discordia

  • Please do not post comments as answers. – Conifold Jan 23 '18 at 21:54
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it's a true sentence since the fact that they have nine toes isn't false. Yes, it can trick someone but it's still true.

  • What do you mean because the sentence s not false it must be true? So reasoning like this means that if something is not illegal it must be legal? Becasue the woman never said no to my sexual advance it must be that she said yes? – Logikal Oct 26 '17 at 18:51
  • I agree with Logikal. – Mark Andrews Oct 27 '17 at 21:35

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