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‘Aristotle was great’. Is this a statement?

I consider a statement to be something either true or false (but not both).

For an individual, this may be considered a statement (because either you think the statement is true or it is false, assuming that an indifferent opinion is counting as thinking he is not great).

However, as a collective, this may not be considered a statement because some people will say its true and some will say its false, going against the definition that a statement cannot be both.

So, is ‘Aristotle is great’ considered a statement?

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    You are confusing math terminology to the real world. A statement doesn't have to be true or false. Some statements are meaningless for instance. Propositions are what is expressed to be true or false. Propositions are ideas in the mind expressed through a language for others to know the idea. This means meaningful declarative sentences in English. So you may hear people say declarative sentences are true or false. Propositions are not sentences. Sentences can be seen, written, etc. An opinion in many cases is a statement. "Mayweather is the best pound for pound boxer ever" is a statement. – Logikal May 28 at 19:05
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    Interestingly, this question was sparked from a book of mathematical thinking (but didn’t think this question would be entirely appropriate to the maths stack exchange) It is quite interesting to see the varying viewpoints from a mathematicians viewpoint and one of a philosopher. – Jamminermit May 28 at 19:09
  • A statement in logic is something that is unambiguously true or false. It doesn't matter if it is only an opinion (because we do not know, or even can not know), but its truth/falsity has to be, in principle, definitive. Sentences involving vague predicates, like "great", "beautiful", "interesting", are not statements in this narrow sense. When someone says "Aristotle was great" they are typically not applying any definitive criteria, even subjective ones, but only conveying a vague impression. In contrast, "Aristotle was heterosexual" is a statement, even though we'll never know for sure. – Conifold May 28 at 22:11
  • I like your way of thinking. "In mathematical logic, a sentence of a predicate logic is a boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false." en.wikipedia.org/wiki/Sentence_(mathematical_logic) – polcott May 30 at 15:35
  • This means that a statement must definitely resolve to true or false, matters of opinion to the contrary carry no weight. Before Pythagoras everyone in the world agreed that the Earth is flat. We know now (from pictures from space) that the Earth is spherical, none-the-less prior statements were eventually resolved to definitely false. – polcott May 30 at 15:38
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Statements (as Kant suggests) have the form subject + predicate. Following the systems theory, this is essentially a semantic interrelation between two systems, which in this case are concepts:

[Aristotle] <--> [Great]

Statements have necessarily such structure. The rest of the elements of a sentence are just the syntactic and lexical auxiliaries. "Jogging" or "tea" are not statements, just concepts.

Moreover, a) the relationships within a sentence are formed not by two systems, but properly, by a subject and an object. No statement exists that don't relate a subject and an object. It could seem that statements like "GOTO 10" (a Basic programming language statement) or "Walk!" don't relate two systems, but that's just apparent. b) The relationships are just interactions (or interaction sets) between the two objects. c) Subject + Predicate means that the predicate is formed by an interaction (or relationship) and an object. Concepts, predicates, subject, object are deeply analyzed in Kant's Critique of Pure Reason.

Examples:

  • "Walk!" is an imperative sentence. This is equivalent to say "You, walk". We don't say "You" because of the language structure, which makes that unnecessary: the subject in an imperative is always the person target of the imperative command. Now, which is the object? When we act, we don't just act. When we clean, we need to clean something. Walking is the same: we act over something. When we walk, we can say that "we walk the walk". Therefore, this sentence is telling "You (subject), do walk (the walk)". The interaction is the first walk.

  • "GOTO 10" is telling the computer (subject) to GO TO [line 10] (object). The relationship or interaction is "going". This is another example of imperative.

  • "Hello" probably means telling "I (subject) am starting the communication with YOU (object)". (And "bye" is used to close the communication)

  • "Please close the door": Subject is you, object is the door, the interaction between both systems, you, and the door, is the act of opening.

  • "Aristotle was great": this is equivalent to say "there's an interaction of the type 'being' between the subject Aristotle and the object Greatness".

Now, to answer your question: opinions have the same structure as propositions and statements. When you say that something is "true or false" you are not adding any valuable information. That's like saying that things are heavy or not. The degree of falsehood or truthfulness is irrelevant. So, they are effectively statements.

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  • You are confusing declarative sentences with statements. Just because statements have the form subject + predicate, it doesn't mean that all sentences of such form are statements. In logic, statements are declarative sentences that are either true or false but not both. "Aristotle was great" is a declarative sentence but it is merely an opinion with no definite truth value. To say something is heavy or not is an opinion just the same. – gadfly Jun 8 at 17:30
  • @gadfly, any type of sentence carries information, regardless of the communication sense. My examples deal explicitly with imperatives and declaratives, but might work well for exclamatives. In any case, I'm not only addressing specific types of sentences, but all statements in general, which are the OP's target. – RodolfoAP Jun 8 at 18:00
  • What you say is irrelevant. Imperatives are not statements. Some declarative sentences are statements and some are not. statements ⊂ declarative sentences ⊂ sentences. Imperative sentences ⊂ sentences. Imperative sentences ⋂ statements = ∅. – gadfly Jun 8 at 20:14
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Strictly speaking it's an opinion and not a statement, unless there is some specific unambiguous definition of "great" that is all agreed on. Just like sentences such as "John is smart" or "Ann is pretty" are opinions and not statements, unless there are specific unambiguous standards of "smart" and "pretty", resp.

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  • Interesting. What is the "unambiguous standard" for 1 meter? Being the standard for 1meter = 1.000000000(infinite number of zeros)m, a ruler measuring 1.00000002m is not a "one meter ruler". Therefore, saying "this ruler measures one meter" is in all cases an opinion, and never ever a statement, since one can always find an ambiguous value just by using more digits. Conversely, if you accept that a meter is a range around 1+/-0.0001m, is that a standard? Accepted by which standards association? You mean that statements don't exist? – RodolfoAP Jun 8 at 20:38
  • Futile for me to continue here. I refer you to some introductory logic books. Also, the comment by Conifold above is close to what I mean, with the exception where he/she said it doesn't matter if it's an opinion. – gadfly Jun 8 at 23:22

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