No other boy in the team is a better player than Tom

[jutfrank]

I'd expect "No other boy is as good as Tom is" to be commonly understood as "Every other boy is worse than Tom is",

Correct. That's what it means in ordinary language.

but in logic, only to mean "Every other boy is either better or worse than Tom, just not equally good".

What do you mean by 'in logic'? If this were the case, a logician would write such a proposition in logical form to make the meaning unequivocal.

[Glizdka]

What do you mean by 'in logic'? If this were the case, a logician would write such a proposition in logical form to make the meaning unequivocal.

You caught me off guard. I know logic only from math.

Can I do like a mathematician would?

[jutfrank]

What do you mean?

[Glizdka]

I used the word logic a bit too carelessly. When you said about a proposition in logical form, I realized I couldn't deliver. I've never studied logic except for in math.

Would a semanticist understand a mathematician?

---

let:
T - team, set of boys
a - Tom, a boy
x - boy other than Tom
prowess at sport be value of variable

T={a, x1, x2, x3, ... xn-1}
a∈T
x∈{T\a}

---

"No other boy is a better player than Tom" means "Every other boy is worse than Tom" and "Tom is the best boy in the team".

∀x∈{T\a}:x≯ a ↔ x<a ↔ a>x

---

"No other boy is a better player than Tom" means "Every other boy is either worse than or as good as Tom", but it doesn't imply that "Tom is the best boy in the team" because "There may be a boy in the team that is as good as Tom".

∀x∈{T\a}:(x≯ a ↔ x≤a ↔ x<a ∨ x=a) ↛ a>x ∵ ∃'x∈{T\a}:x=a

---

"Tom is the best boy in the team" implies that "No other boy in the team is a better player than Tom".

∀x∈{T\a}:a>x → x≯ a

[jutfrank]

I'm not sure what you're asking or why, Glizdka.

What is it that you're trying to learn with all this?

[Glizdka]

I've reworked post#14. It was unreadable. I hope it's clearer now.

I'm not sure what you're asking or why, Glizdka.

What is it that you're trying to learn with all this?

Are these true?

A) "No other boy is a better player than Tom" means "Every other boy is worse than Tom" and "Tom is the best boy in the team".
B) "No other boy is a better player than Tom" means "Every other boy is either worse than or as good as Tom", but it doesn't imply that "Tom is the best boy in the team" because "There may be a boy in the team that is as good as Tom".
C) "Tom is the best boy in the team" implies that "No other boy in the team is a better player than Tom".

[Rover_KE]

Is anybody else's head spinning?

[jutfrank]

You're not using the word imply quite right. What you mean is entail.

[Glizdka]

C) It does not just imply that.

You're not using the word imply quite right. What you mean is entail.

I've changed imply to entail. Are these true?

C1) "Tom is the best boy in the team" entails "No other boy in the team is a better player than Tom".
a>x → x≯ a

C2) "No other boy in the team is a better player than Tom" doesn't entail "Tom is the best boy in the team".
x≯ a ↛ a>x

[Tarheel]

I know what sentence we're discussing. I also know it's rather unnatural. If somebody wants to say Tom is the best player on the team they will usually say exactly that. "Tom is the best player on the team" leaves no doubt about what is meant, and it is the normal way to say it. Since this is an ESL website, I would encourage people to say it that way.