View Poll Results: Do you think all these arguments are valid, only some are, or none of them?

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• All these arguments are valid

1 16.67%
• Only some of these arguments are valid

1 16.67%
• None of these argument is valid

3 50.00%
• I don't know

1 16.67%
• These arguments don't make sense.

0 0%

Thread: All; therefore some?

1. Originally Posted by Jokodo
Even if we treat ALL A as always carrying an existential presupposition as an integral party of its meaning,
But in this case, isn't the implication "all x is F; therefore some x is F" valid?

Originally Posted by Jokodo
it doesn't become false of an empty set - it gets an undefined truth value, requiring a trivalent logic. It's what being a presupposition means: the negation of a statement does not imply the negation of the its presuppositions. In order for "the king of France is bald" to be either true or false in most modern implementations of logic, there has to be a French king.
Yet, it seems that when we say "all angels have wings", we assume there are angels. It is just a case of mathematicians being unable to produce a correct model of the deductive logic of human beings.
EB

2. Originally Posted by Jokodo
Originally Posted by Speakpigeon
Originally Posted by Jokodo

It's how we have defined ALL to operate, in order to achieve full equivalence between ALL and NOT ANY NOT. It is intuitively clear that ALL A P implies NOT ANY A NOT P. Except for this particular corner case where there are no As, the reverse is also clearly true. We lack however clear intuitions for what should be the truth value of ALL A said of an empty set A. Defining it in such a way that it's always true allows for a simple, mechanic check: ALL A ARE P is false if and only if there is at least one A that isn't P. This leads to an overall more elegant and consistent system.
No, I mean, can you justify that "all" and "some" are used in English only in the way that you imply here?
EB
I cannot justify something I never claimed. You asked about logic and implication, not about any and all ways English speakers use a particular word. I believe I bade clear I'm taking about the concept and not the word by using all caps.

There is an argument to be made that the pure semantics of the English word is indeed very much parallel to the abstract concept and any meanings beyond that it customarily receives is in the domain of pragmatics, for a quick sketch of which I refer you to my last post - but it's not an argument I made in the post you replied to.
Good, so you accept that you couldn't justify that usage carries the implications accepted in mathematical logic?
EB

3. Originally Posted by Speakpigeon
Originally Posted by Jokodo
Even if we treat ALL A as always carrying an existential presupposition as an integral party of its meaning,
But in this case, isn't the implication "all x is F; therefore some x is F" valid?
It would be, yes. But that would require a non- classical trivalent logic and the additional assumption that the existential presupposition is actually part of the semantics of "all" and not a pragmatic import, something you haven't shown, and won't be able to unless you get a good grasp of the difference between semantics and pragmatics.

Originally Posted by Jokodo
it doesn't become false of an empty set - it gets an undefined truth value, requiring a trivalent logic. It's what being a presupposition means: the negation of a statement does not imply the negation of the its presuppositions. In order for "the king of France is bald" to be either true or false in most modern implementations of logic, there has to be a French king.
Yet, it seems that when we say "all angels have wings", we assume there are angels. It is just a case of mathematicians being unable to produce a correct model of the deductive logic of human beings.
EB
Looks more like a case if you misunderstanding the scope and purpose of logic from where I am standing.

4. Originally Posted by Speakpigeon
Originally Posted by Jokodo

I cannot justify something I never claimed. You asked about logic and implication, not about any and all ways English speakers use a particular word. I believe I bade clear I'm taking about the concept and not the word by using all caps.

There is an argument to be made that the pure semantics of the English word is indeed very much parallel to the abstract concept and any meanings beyond that it customarily receives is in the domain of pragmatics, for a quick sketch of which I refer you to my last post - but it's not an argument I made in the post you replied to.
Good, so you accept that you couldn't justify that usage carries the implications accepted in mathematical logic?
EB
In classical mathematical logic, it does. What some word that in writing looks similar to the logical operator ALL may or may not mean is a different discussion.

I did however sketch an argument that English "all" and logic ALL are more similar than they seem at first sight, with the difference being in the pragmatic domain.

You haven't even tried to show that they are different.

5. It's actually fairly easy to construe contexts where the existential presupposition doesn't appear to hold. E.g., a lecturer announcing that she won't start the class until all cell phones are turned off is unlikely to cancel the class when she finds that no one brought their phone, and police during a surprise inspection of a company demanding that all foreign workers show their work permits won't hand out penalties when they find the company only employs domestic workers. Even intuitively, a situation where there are no phones qualifies as one where all phones are turned off, or one where there are no foreign workers as one where they've all successfully produced their work permits. The fact that the existential presupposition as an apparent component if the meaning of "all" can be so easily ignored given proper context is actually a telltale sign of its pragmatic nature, making your job of demonstrating that it is semantic rather unfeasible.

6. Originally Posted by Speakpigeon
Yet, it seems that when we say "all angels have wings", we assume there are angels.
We assume that more often than not - because talking of the properties of nonexistent entities rarely makes sense. But that's a fact about the psychology of communication, or pragmatics as we call it. It is not a fact about the meaning of the English word "all" or the logical operator ALL, and does thus not demonstrate a mismatch between the two. And if it did, it still wouldn't make either of them useless.

7. Originally Posted by Jokodo
It would be, yes. But that would require a non- classical trivalent logic and the additional assumption that the existential presupposition is actually part of the semantics of "all" and not a pragmatic import, something you haven't shown, and won't be able to unless you get a good grasp of the difference between semantics and pragmatics.
Ad hominem.

Originally Posted by Jokodo
Looks more like a case if you misunderstanding the scope and purpose of logic from where I am standing.
I don't care where you are standing. I asked a question, you provided an opinion you can't support from empirical evidence.

Fine with me.
EB

8. Originally Posted by Jokodo
In classical mathematical logic, it does.
I didn't ask any question about mathematical logic.

Originally Posted by Jokodo
You haven't even tried to show that they are different.
Whoa!!! It is for me to disprove that God exists?

And I thought I was asking a question. Now I have to provide the answer, too.
EB

9. Originally Posted by Jokodo
It's actually fairly easy to construe contexts where the existential presupposition doesn't appear to hold. E.g., a lecturer announcing that she won't start the class until all cell phones are turned off is unlikely to cancel the class when she finds that no one brought their phone,
You think the lecturer would have to conclude turned off cell-phones don't exist?!

Originally Posted by Jokodo
and police during a surprise inspection of a company demanding that all foreign workers show their work permits won't hand out penalties when they find the company only employs domestic workers.
You think the police would have to conclude foreign workers don't exist?!

Originally Posted by Jokodo
Even intuitively, a situation where there are no phones qualifies as one where all phones are turned off,
Intuitively, certainly not.

Originally Posted by Jokodo
or one where there are no foreign workers as one where they've all successfully produced their work permits.
Intuitively, certainly not.

Originally Posted by Jokodo

The fact that the existential presupposition as an apparent component if the meaning of "all" can be so easily ignored given proper context is actually a telltale sign of its pragmatic nature, making your job of demonstrating that it is semantic rather unfeasible.
I don't have a job here. I asked a question, you provided an opinion that you cannot support from empirical evidence.
EB

10. Anyway, thanks for your patience, but I think we don't need to pursue this conversation. You've said what you could.
EB

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