There is no logical symbol for “ARE” — I like sushi


Then why ask? If your book shows an example and says “are” - in the example given - means implied, then you had your answer before you posted here? I was simply saying “are” is not a logical symbol (in predicative or propositional notation).

All sorted? — I like sushi


You were simply stating that there is no logical symbol for "ARE."
This is not equivalent to the claim that “are” is not a logical symbol. I mean yeah, of course, a word is not a logical symbol.

I didn't ask if it's true that there is no logical symbol for "ARE." You said that there is no logical symbol for "ARE" and I, therefore, claimed that you're wrong.

I asked, for example, the following:

Is there a convention in logic for how "cats are yellow" should be interpreted? — Jimmy1


That is, is it true that?

When we don't explicitly state a quantifier (all/some) then it's assumed that the statement is a universal. — TheMadFool


If you are educated in predicate logic or not is actually relevant to that question (given the quote below), but you don't to answer the question: "Are you educated in predicate logic aka first-order logic?"

↪Jimmy1
Not that I can see? I’d expect an “ALL”/“SOME”/“NONE” before. Without a quantifier there is nothing to work with. — I like sushi


Not all is sorted. Since I can't find a source on it, I still don't know for sure if it's true that:

When we don't explicitly state a quantifier (all/some) then it's assumed that the statement is a universal. — TheMadFool

You could, by your argument, also insist that IF means (“If it is such that said item ‘p’ is true then it follows in such a way that q is implicated by the being of p.”) — I like sushi

That is false if we use the conventions of logic. Because if it is that p is true, then it is not necessarily the case that q is true. Therefore it's false that "If it is such that said item ‘p’ is true then it follows in such a way that q is implicated by the being of p"

Also, this is not what I've done. I've quoted an argument, from a textbook (that deals with this very topic), that shows that "are" is written to mean implication in predicate logic. I've given you the evidence of the convention of that in logic, "are" is allowed to be translated to mean implication (actually, it's allowed in predicate logic at least)

I think you are confusing predicate logic with propositional logic. Are you educated in predicate logic aka first-order logic?

You could, by your argument, also insist that IF means (“If it is such that said item ‘p’ is true then it follows in such a way that q is implicated by the being of p.”). — I like sushi

That is false if we use the conventions of logic. Because if it is that p is true, then it is not necessarily the case that q is true. Therefore it's false that "If it is such that said item ‘p’ is true then it follows in such a way that q is implicated by the being of p"

Also, this is not what I've done. I've quoted an argument, from a textbook, that shows that "are" is written to mean implication in predicate logic. I've given you the evidence of the convention of that: in logic, "are" can be translated to mean implication.

I think you are confusing predicate logic with propositional logic. Are you equated in predicate logic aka first-order logic?

All ravens are black.
There exist ravens in Sweden.
Therefore, there exist black animals in Sweden.

K(x): x is a raven
S(x): x is a black animal
H(x): x is an animal is Sweden

For All x: [K(x)->S(x)]
There exists x such that: [(k(x) and H(x)]
Therefore, there exists x such that: [S(x) and H(x)] — Jimmy1

All ravens are black is translated to symbolic logic as: For all x: [K(x)->S(x)].
Therefore, the implication symbol is used for "are."
Directly translated back to "normal language", For all x:[K(x)->S(x)] means: For all x, if x is a raven, then x is a black animal.
In first-order logic, you are evidently allowed to assume that all ravens are animals.

I edited and changed "there exist birds in Sweden" to "there exist black animals in Sweden", btw, to make the argument consistent with the symbolic argument. I made a whoopsie.

There is no logical symbol for “ARE”. End of story.

Anything else is merely a question of semantic interpretation to set out logical propositions. — I like sushi

Well, that is what's bothering me, because it's false that there is no logical symbol for are.
And that's why I said what I said in the previous post. I provided evidence, from a textbook on mathematical logic, that it's false that there is no logical symbol for are.

Cats are yellow = ALL cats are yellow — TheMadFool

What I wanna know is if, in logic, "cats are yellow" should be interpreted as "all cats are yellow." — Jimmy


Oh, sorry. I just read the OP and was a little puzzled by what was confusing you. — I like sushi

You two are in disagreement here. Why is he wrong? Can you deduce it? Can you source it?

I edited and changed "there exist birds in Sweden" to "there exist black animals in Sweden", btw, to make the argument consistent with the symbolic argument. I made a whoopsie.

There is no logical symbol for “ARE”. End of story.

Anything else is merely a question of semantic interpretation to set out logical propositions. — I like sushi

Well, that is what's bothering me, because it's false that there is no logical symbol for are.
And that's why I said what I said in the previous post. I provided evidence, from a textbook on mathematical logic, that it's false that there is no logical symbol for are.

Cats are yellow = ALL cats are yellow — TheMadFool

What I wanna know is if, in logic, "cats are yellow" should be interpreted as "all cats are yellow." — Jimmy


Oh, sorry. I just read the OP and was a little puzzled by what was confusing you.

No, it shouldn’t. — I like sushi

You two are in disagreement here. Why is he wrong? Can you deduce it? Can you source it?

I edited and changed "there exist birds in Sweden" to "there exist black animals in Sweden", btw, to make the argument consistent with the symbolic argument. I made a whoopsie.

There is no logical symbol for “ARE”. End of story.

Anything else is merely a question of semantic interpretation to set out logical propositions. — I like sushi

Well, that is what's bothering me, because it's false that there is no logical symbol for are.
And that's why I said what I said in the previous post. I provided evidence, from a textbook on mathematical logic, that it's false that there is no logical symbol for are.

Cats are yellow = ALL cats are yellow — TheMadFool

What I wanna know is if, in logic, "cats are yellow" should be interpreted as "all cats are yellow." — Jimmy


Oh, sorry. I just read the OP and was a little puzzled by what was confusing you.

No, it shouldn’t. — I like sushi

You two are in disagreement here. Why is Themadfool wrong? Can you deduce it? Can you source it?

Well, I wouldn't say I have found an exception to the rule that A are B is equivalent to All A are B (if it is a rule). It could just be the case that it's not true that cats are four-legged animals. The conclusion doesn't really jive with me, but it would be true if the rule is true.

I don't know what you mean. Interpreting if "a, then b" as "a->b" is also a semantic interpretation since the interpretation is related to meaning in logic. It just happens to be the case that the convention in logic is to interpret "if a, then b" as "a->b". But nonetheless, there is a logical symbol for "if a, then b."
There is also a convention for which logical symbol to use for "all a are b."

Here's an argument using "are," directly from a textbook, and the logical symbol that is used for "are":

All ravens are black.
There exist ravens in Sweden.
Therefore, there exist black animals in Sweden.

K(x): x is a raven
S(x): x is a black animal
H(x): x is an animal is Sweden

For All x: [K(x)->S(x)]
There exists x such that: [(k(x) and H(x)]
Therefore, there exists x such that: [S(x) and H(x)]

I was watching a youtube video made by a mathematician. He claimed that it's true that cats are four-legged animals, and that the definition of four-legged is: have four legs.

But suppose that the proposition that cats are four-legged animals is equivalent to the proposition that all cats are four-legged animals.
If the propositions are equivalent, and if it's true that cats are four-legged animals, then it's true that all cats are four-legged animals.
But suppose the aforementioned statements are equivalent and suppose that all cats are four-legged animals, then it's true that if something is a cat, it's necessarily a four-legged animal.
But it's actually false that if something is a cat, then it's necessarily a four-legged animal. For example, there are cats that are not four-legged animals.
And so, If it's true that the aforementioned statements are equivalent, it's therefore false that cats are four-legged animals, and the mathematician would be wrong. This conclusion doesn't really jive with me, so I want to know for sure if it's true that "Cats are yellow = ALL cats are yellow"

But I do think it's true that:

When we don't explicitly state a quantifier (all/some) then it's assumed that the statement is a universal. — TheMadFool

Is there a convention in logic for how "cats are yellow" should be interpreted?

You can say that all cats are yellow as a logical premise. Did something lead you to believe that I don't believe that?

What I wanna know is if, in logic, "cats are yellow" should be interpreted as "all cats are yellow."

If it's not specified that all cats are yellow, and not specified that some cats are yellow, and not specified that no cats are yellow, then what does "cats are yellow" mean? Does it mean all cats are yellow? Does it mean some cats are yellow? Does it mean no cats are yellow? Does it mean something else? Does it mean nothing? What is the convention in logic?

A valid argument is an argument where the premises forces the conclusion to be true. A sound argument is an argument that is valid and the premises are true.