# All; therefore some?

## Do you think all these arguments are valid, only some are, or none of them?

• ### I don't know

• Total voters
2
• Poll closed .

#### Speakpigeon

Valued Senior Member
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

All of the arguments are valid. Therefore some of the arguments are valid. Also, any of the arguments is valid, each of the arguments is valid, etc. It's more a question of language than of logic.

All of the arguments are valid. Therefore some of the arguments are valid. Also, any of the arguments is valid, each of the arguments is valid, etc. It's more a question of language than of logic.
Thanks.
Yes, the semantics of "all" and "some" is crucial here. However, it is still a question of logic.
EB

If all arguments are valid, then some arguments are valid
then all of these argument are valid and therefore this argument is valid

insofar as a
statement of opinion
is an argument

If all arguments are valid, then some arguments are valid then all of these argument are valid and therefore this argument is valid
insofar as a statement of opinion is an argument
You think that the conditional "If all arguments are valid, then this argument is valid" is an opinion?!
EB

You think that the conditional "If all arguments are valid, then this argument is valid" is an opinion?!
EB
No. I think that

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.
are opinions. No "if", and since the word "all" contains smaller collective units [some, any, many, most] by definition, the second statement in each set is merely redundant. No argument is presented.

And no reply was posted. Which is just as well.
EB

Doesn' t the use of the word "some" imply "some but NOT all"?

The term some is relative
The term All is absolute
Is mixing these valid?

example:
All people are human, therefore most people are human. Is mixing relative terms with absolute terms.
To state that "most people are human" in isolation is incorrect IMO.

Doesn' t the use of the word "some" imply "some but NOT all"?
Exactly. All, by definition, includes every relative collective term. Proceeding from the whole to the part is not an argument; it is a mere redundancy.

Try,
All people are mortal, therefore some are mortal.
Implying that some are not mortal.
By specifying some as mortal it implies that some are not.

By specifying some as mortal it implies that some are not.
Not necessarily, and at least not when discussing logic.
E.g. All people are mortal, therefore some people are mortal... and so are the rest.
In logic, “some” just refers to an unspecified number/amount of a thing, and possibly all.

As such, if one takes validity to be defined by it being impossible for the premise to be true yet the conclusion false, then the form expressed in the OP is indeed valid: if “all X are Y” is true then it is impossible for “some X are Y” to be false.

In common language, however, we might use “some” as a quantifier that covers the ground between the extremes of “none” and “all”.
But this is different to its meaning in logic.

Not necessarily, and at least not when discussing logic.
E.g. All people are mortal, therefore some people are mortal... and so are the rest.
In logic, “some” just refers to an unspecified number/amount of a thing, and possibly all.

As such, if one takes validity to be defined by it being impossible for the premise to be true yet the conclusion false, then the form expressed in the OP is indeed valid: if “all X are Y” is true then it is impossible for “some X are Y” to be false.

In common language, however, we might use “some” as a quantifier that covers the ground between the extremes of “none” and “all”.
But this is different to its meaning in logic.
If we assume your interpretation of the word some then I would contend that:
If the statement presents no argument then it is not an argument therefore invalid as an argument.
There is no argument as it is merely a repetition, a redundant and unnecessary inclusion.

Like stating the following:
If A=B and A=B then A=B
To me this is not an argument but I will accept that the nuances of formal logic may suggest other wise.
If A= B and B= C then A =B
Is also not an argument.
Does that make sense?

If one states that the following is definitely an argument:
If all humans are mortal then some humans are mortal, and continues to consider it an argument when it isn't, then I would consider it as invalid because it implies that some humans are not mortal as it is arguing that only some are mortal.So if you ask if this is a valid argument I would say no it isn't.
But again the nuances of formal logic may say other wise...

Summary:
In both cases the statement is invalid as an argument.
For the following reasons:
That it is merely an affirmation of the premise and offers no argument.
A=B then A=B
That if it is offered as an argument and is not merely an affirmation of the premise it is invalid because it fails to rule out an alternative to the premise.
A=B and some of A = B therefore some of A could =/= B
Of course the nuances of formal logic may say otherwise...

Last edited:
If we assume your interpretation of the word some then I would contend that:
If the statement presents no argument then it is not an argument therefore invalid as an argument.
There is no argument as it is merely a repetition, a redundant and unnecessary inclusion.
There is an argument, though: at least one premise, followed by a conclusion drawn from those premises.
This is what constitutes an argument.
Like stating the following:
If A=B and A=B then A=B
To me this is not an argument but I will accept that the nuances of formal logic may suggest other wise.
It is a valid argument, and question begging twice over.
But it is an argument nonetheless.
It is not a nuance of formal logic, but simply the definition of what an argument is.
If A= B and B= C then A =B
Is also not an argument.
Does that make sense?
Again, it is an argument, it is valid, and it also begs the question.
But it is still an argument, this time with a redundant premise.
If one states that the following is definitely an argument:
If all humans are mortal then some humans are mortal, and continues to consider it an argument when it isn't, then I would consider it as invalid because it implies that some humans are not mortal as it is arguing that only some are mortal.So if you ask if this is a valid argument I would say no it isn't.
But again the nuances of formal logic may say other wise...
It is an argument, and it is, according to the usual (in logic) definition of validity, a valid argument.
Not a nuance, but rather a somewhat unsubtle difference to what you consider an argument, or validity, to be.

Last edited:
Try,
All people are mortal, therefore some are mortal.
Implying that some are not mortal.
By specifying some as mortal it implies that some are not.
Some definitions:
some -- Wiktionary
1. A certain number, at least one.
Some enjoy spicy food, others prefer it milder.
2. An indefinite quantity.
Can I have some of them?
3. An indefinite amount, a part.
please give me some of the cake;
everyone is wrong some of the time

SOME, adjective sum. -- Webster's Dictionary 1828
1. Noting a certain quantity of a thing, but indeterminate; a portion greater or less. Give me some bread; drink some wine; bring some water.
2. Noting a number of persons or things, greater or less, but indeterminate. some theoretical writes allege that there was a time when there was no such thing as society.
3. Noting a person or thing, but not known, or not specific and definite. some person, I know not who, gave me the information. Enter the city, and some man will direct you to the house. Most gentlemen of property, as some period or other of their lives, are ambitious of representing their country in parliament.
EB

From the nice picture you posted, how do you conclude that the following is not an argument?

A = B;
A = B;
Therefore, A = B.

Premises, true or false, conclusion follows from the premises. What's missing?
EB

From the nice picture you posted, how do you conclude that the following is not an argument?

A = B;
A = B;
Therefore, A = B.

Premises, true or false, conclusion follows from the premises. What's missing?
EB
Having not formally studied logic I am not familiar with the precise terminology needed to explain my point.
Should an argument extend beyond the premise or is the premise the conclusion?
To me the conclusion has to be an outcome of the premise and not simply the premise.

It is important I feel, in these types of discussions to always include the operators etc in the form.

IF A=B
AND A= B
THEREFORE A=B

Offers no argument because the premise is the conclusion and not an outcome of the conclusion. A false argument perhaps? An argument over nothing...?
Simply stating A=B would be sufficient. There is no supporting A=B. It is a statement of "authority" and no argument is offered.

"An argument is :
a collection of statements (premises) intended to support or infer a claim ( conclusion)"
(from the image file I posted)

A=B because A=B, offers no argument to support the conclusion. It is a statement of unsupported "authority".
A=B because C=D does offers an argument but is unsupported...It is a statement of unsupported "authority" - Begging the question?
I am not convinced that, as Baldeee maybe correctly suggesting, that it is Begging the question but an argument regardless. I may have to accept that to be the case though.
In the context of this discussion the issue is not so clear IMO.
So to me the issue boils down to a very fine line between what an argument is and what it is not.
Simply using words like If , Therefore, Because - do not alone establish an argument.

However, an argument of what I would call "reciprocal equivalence" could be stated as:
IF A=B
and B=A
THEN A=B

The difference is subtle but an argument is established and is sound. IMO.
=====
What actual argument is offered according to you?
with your
A=B
A=B
Therefore A=B

Last edited:
To me the conclusion has to be an outcome of the premise and not simply the premise.
An argument that begs the question is one where the conclusion is contained within a premise.
But it is still an argument.
It is important I feel, in these types of discussions to always include the operators etc in the form.
Not all arguments have or need such operators.
In classical syllogisms one merely states the premises, and one takes them as being true for purposes of reaching a deductive conclusion from those premises.
Hence:
All men are mortal.
Socrates is a man.
Hence Socrates is mortal.
This is a valid argument.

IF A=B
AND A= B
THEREFORE A=B

Offers no argument because the premise is the conclusion and not an outcome of the conclusion. A false argument perhaps? An argument over nothing...?
Simply stating A=B would be sufficient. There is no supporting A=B. It is a statement of "authority" and no argument is offered.
the support in the argument for the conclusion that A=B is the premise that A=B.
The conclusion is based entirely on this.
It begs the question, and is thus worthless as an argument, but it is nonetheless an argument.

"An argument is :
a collection of statements (premises) intended to support or infer a claim ( conclusion)"
(from the image file I posted)

A=B because A=B, offers no argument to support the conclusion. It is a statement of unsupported "authority".
What could support the conclusion more than a premise that states it explicitly?
You seem to grasp that it is worthless as an argument, but it is still an argument.
A=B because C=D does offers an argument but is unsupported...It is a statement of unsupported "authority"
This is an argument, it doesn't beg the question, but is invalid (in that the premise could be true yet the conclusion nonetheless false).
I am not convinced that, as Baldeee maybe correctly suggesting, that it is Begging the question but an argument regardless. I may have to accept that to be the case though.
In the context of this discussion the issue is not so clear IMO.
The first begs the question, the second does not.
And in the context of this discussion it is rather clear.

So to me the issue boils down to a very fine line between what an argument is and what it is not.
Simply using words like If , Therefore, Because - do not alone establish an argument.
There are many ways of formulating arguments, but if used correctly, the trigger words like "therefore" and "because" do indicate the presence of an argument.
However, an argument of what I would call "reciprocal equivalence" could be stated as:
IF A=B
and B=A
THEN A=B

The difference is subtle but an argument is established and is sound. IMO.
It is certainly an argument, but it begs the question just as much as if you had omitted the "and B=A".
It is also not sound, although it is valid.
Soundness relates to whether the premises are true in reality.
You have to define what A and B are before you can judge soundness.
Validity is a matter of the form of the argument.
What actual argument is offered according to you?
with your
A=B
A=B
Therefore A=B
The argument is that we can conclude that A=B is true because we have taken as true the premise that A=B.
It begs the question but is a valid argument.

What could support the conclusion more than a premise that states it explicitly?
You seem to grasp that it is worthless as an argument, but it is still an argument.
"A collection of statements" means what to you?
It means more than one to me...

Just to help clarify your position:
is:
A = A
an argument?