Does the word "can" indicate a relationship?

Giant Panda

Hi all,

Just a quick question, does the word "can" indicate a relationship or is it indicate like "could", "might" a probability?

For instance, the sentence, "Some reporters can scoop all of the reporters", can you translate it into: Reporter X<-Some->Scoop all of the reporters. Or is it just a statement indicating probability of this relationship?

if that is not true, then, as a rule of thumb, you can never translate a probabilistic statement into a conditional statement since conditional statement are 100% of occurrence?

inactive

Edited your title a bit so it was more clear.

Heart Shaped Box

I don't think it does, at least not a conditional one. Because an universal quantifier/conditional logic dictates a logical relationship between the sufficient and necessary condition. Its a relationship of a complete subsumption. The sufficiency "implies" the necessary, to "quantify the entire universe of a subset". But if you say "Some reporters can scoop all of the reporters" while it may be understandable within the flexibility of the English language, I wouldn't know how to represent this idea with universal quantifier/conditional logic. Cuz it's not really "conditional".

The difference for existential quantifier is the latter speaks for an intersection. Such as some, most, none, etc. Does this sentence express an intersection/overlapping relationship? So if we say "some dogs are cute" then we know it's speaking for a range from 1 to all the way 100, thus the intersection could be anywhere along the line. Bc we know its "existence" has been defined. But if we say "Some reporters can scoop all of the reporters", we cannot translate this with existential quantifier, bc its existence is not definitively defined. All we know is some can scoop all of them, but what does that mean in logic?

I definitively understand where you are coming from and the trickiness of this statement. I think it's a perfectly okay expression in the English language, it's expressing the "capability/probability" of a subset of doing something. I just don't know if we could adequately express this idea with the logic language such as universal/existential quantifier, bc it neither dictates a conditional relationship nor an intersection, at least not for the world of the LSAT as far as I know. But then again, what the heck do I know? lol Just a personal perspective based on my very limited knowledge, any input would be greatly appreciated.

Giant Panda

This is great input. I went into modal logic.

It's theory is one much like yours.

JustDoIt

I think @"Heart Shaped Box" nailed it. With both universal and existential quantifiers, we know that something is definitively happening. With conditional relationships, the sufficient guarantees a result i.e. the necessary condition. Same with failing the necessary which guarantees that sufficient will fail. Either way, we know that some result will follow in either case. Even with some relationships, we know at least 1 is included. With "can," do we know if anything will actually happen? No, we don't. I can drive across the country. But will I?

Capability is no different from possibility. Something could happen but will it? We just don't know. We would not say because something could possibly happen that there is a conditional relationship there. In our language of lawgic, there is no way to even illustrate this mere chance. So we have to say that "can" does not indicate a relationship.