All; therefore some?

[Speakpigeon]

Ah, here is a very interesting piece of logic. I give the general form of the argument first, and then three straightforward applications of the general form.

All A's are/have F;
Therefore, some A is/has F.

All angels have wings;
Therefore, some angel has wings.

All politicians are liars;
Therefore, some politician is a liar.

All imaginary beings have serious existential problems;
Therefore, some imaginary being has serious existential problems.

Thank you to say whether you think all these arguments are valid, or only some, or none.

Thank you to cast your vote before posting any comment.
EB

 

[Jokodo]

Ah, here is a very interesting piece of logic. I give the general form of the argument first, and then three straightforward applications of the general form.

All A's are/have F;
Therefore, some A is/has F.

All angels have wings;
Therefore, some angel has wings.

All politicians are liars;
Therefore, some politician is a liar.

All imaginary beings have serious existential problems;
Therefore, some imaginary being has serious existential problems.

Thank you to say whether you think all these arguments are valid, or only some, or none.

Thank you to cast your vote before posting any comment.
EB

It's valid only with the additional premise, (often left unspoken) that As exist. If there ate no As, then "all As P" is trivially true for all predicates P, while "some As" is necessarily false. I believe it's called an existential presupposition.

 

[Bronzeage]

A redundant statement is not an argument just because it includes the word "therefore".

 

[Speakpigeon]

Thanks to posters who have cast their vote.
EB

 

[Speakpigeon]

It's valid only with the additional premise, (often left unspoken) that As exist. If there ate no As, then "all As P" is trivially true for all predicates P, while "some As" is necessarily false. I believe it's called an existential presupposition.

Can you justify this?
EB

 

[Jokodo]

It's valid only with the additional premise, (often left unspoken) that As exist. If there ate no As, then "all As P" is trivially true for all predicates P, while "some As" is necessarily false. I believe it's called an existential presupposition.

Can you justify this?
EB

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.

 

[Jokodo]

Even if we treat ALL A as always carrying an existential presupposition as an integral party of its meaning, 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.

 

[Speakpigeon]

It's valid only with the additional premise, (often left unspoken) that As exist. If there ate no As, then "all As P" is trivially true for all predicates P, while "some As" is necessarily false. I believe it's called an existential presupposition.

Can you justify this?
EB

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

 

[Jokodo]

However most analyses would posit that the existential presupposition is a pragmatic import: people don't generally have a habit of making specific claims of nonexistent entities, so the moment we hear someone talk of ALL As, we conclude they believe in the existence of As and evaluate the rest of their claim under that assumption - even though it is not something they ever claimed explicitly.

 

[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.

 

[Speakpigeon]

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 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

 

[Speakpigeon]

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

 

[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.

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.

 

[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.

 

[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, 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.

 

[Jokodo]

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.

 

[Speakpigeon]

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.

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

 

[Speakpigeon]

In classical mathematical logic, it does.

I didn't ask any question about mathematical logic.

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

 

[Speakpigeon]

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?!

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?!

Even intuitively, a situation where there are no phones qualifies as one where all phones are turned off,

Intuitively, certainly not.

or one where there are no foreign workers as one where they've all successfully produced their work permits.

Intuitively, certainly not.

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

 

[Speakpigeon]

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