After reading the article from Wikipedia I feel more confused on what the scope of the definition of a 'logical statement' or proposition is. First, is the statement "It is raining" considered to be a proposition, or is it too vague because it is devoid of context, such as where and when it is raining?

Second, I don't understand the assertion by this article that the statement "Pegasus exists" may not be a logical statement. Either Pegasus exists or doesn't exist, so how is this not a logical statement?

  • "It is raining (here and now)" is sufficiently definitive to be a statement, "here and now" is implicitly presupposed. Whether Pegasus exists depends on one's definition of "exists" (in reality, as a fiction, mentally, etc.), without specification "Pegasus exists" is too ambiguous to be a statement. Moreover, definitions of existence are controversial, hence its truth value is a matter of opinion.
    – Conifold
    Sep 29 '19 at 21:57
  • @Conifold If we can presuppose information not appearing in a statement (as in the "here and now" for the "It is raining" statement), I would say that "Pegasus exists" is not ambiguous, as "in the physical realm" may be implicitly presupposed. Sep 30 '19 at 9:11
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    That would make it a statement, but it is not the default the way here and now is in "it is X-ing" statements. What is or is not presupposed colloquially is not a matter of logic though, so it makes little difference what resolves the ambiguity, context or stipulation, as long as it is resolved.
    – Conifold
    Sep 30 '19 at 11:50

The basic concept of statement (or proposition) used in logic is the following :

A proposition is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both.

In the context of natural language, the sentence "It is raining" is a declarative sentence stating a fact that is either true or false .

Regarding "Pegasus exists", Wiki's entry says :

Whether or not the sentence "Pegasus exists." is a statement is a subject of debate among philosophers. Bertrand Russell held that it is a (false) statement. Strawson held it is not a statement at all.

The example is a little bit controversial, because it involves a proper name without reference, and this case is a little bit troublesome for standard logic.

We can consider the original Russell/Strawson example :

"The present King of France is bals [wise]."

According to B.Russell in On Denoting (1905) the sentence is significant and false (there is no King of France today), while for Strawson in On Referring (1950) the sentence "is certainly significant; but this does not mean that any particular use of it is true or false."

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    You need to make a distinction between mere existence statements and property statements about questionable objects. 'Fairies exist' — a mere existence claim — is clearly either true or false. 'Fairies own Teslas' is ambiguous because we don't know whether to focus on the 'mere existence' question, or the question of whether non-extant entities can 'own' things. Russell leaned towards commutativity (non-existent things have no properties, and thus property statements are false); Strawson leaned towards the position that we cannot meaningfully talk about the properties of non-extent things. Sep 29 '19 at 11:20
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    Which is to a normal person nonsense because talking with a 5 year old about whether fairies or pegasus have wings is a perfectly natural and meaningful conversation. Non-physical and unrealised concepts can still have properties. If a philosophical framework can't account for a conversation with a 5 year old then IMO it's deficienct. Sep 29 '19 at 12:23
  • A proposition is not a physical sentence. So if I have a declarative sentence in English,French, Italian, Russian, etc how many propositions do I have? There is only one idea expressed. This is why propositions are not literally sentences. Different words can Express the same proposition. The way you have it is that each individual declarative sentence MUST BE a NEW PROPOSITION.
    – Logikal
    Sep 29 '19 at 20:30
  • Thanks for your clarification. I would say I have to disagree with Strawson, but I see the point he's trying to make. While Pegasus may not physically exist, Pegasus does exists in the domain of mythological creatures, and there should be a way we can talk about such a being. Sep 29 '19 at 22:05

Come to think of it, fairies and Pegasus may in fact exist, while Donald Trump maybe doesn't, so that "Donald Trump is the President of the United States of America" would be a more questionable statement.

Most of our logical statements are about things we only believe, indeed that we only imagine, that they exist. Our semantics has better be able to deal with imaginary creatures because most of what we say is about imaginary creatures.

Saying "Pegasus has wings" is logically equivalent to saying "*Pegasus exists and it has wings". And that may be true, and it may be false. We just don't know.

It is also likely that the semantics of "Pegasus has wings" be a bit more subtle than "*Pegasus exists and it has wings", which would account for the fact, indisputable, that most people would blink twice at the statement. However, Wikipedia doesn't appear to know anybody who can explain this subtlety to us, so we will have to wait for Pegasus to explain itself.

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