John Stuart Mill: It must be granted that in every syllogism

[Cindycakes123]

John Stuart Mill wrote:

It must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say,

All men are mortal, Socrates is a man, therefore Socrates is mortal; it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, "Socrates is mortal," is presupposed in the more general assumption, "All men are mortal"; that we can not be assured of the mortality of all men, unless we are already certain of the mortality of every individual man... That, in short, no reasoning from generals to particulars can, as such, prove anything, since from a general principle we cannot infer any particulars but those which the principle itself assumes as known. (from his A System of Logic. Book 2, Chapter 3, Section 2.)



Do you agree? Why or why not?

[Eodnhoj]

John Stuart Mill wrote:

It must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say,

All men are mortal, Socrates is a man, therefore Socrates is mortal; it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, "Socrates is mortal," is presupposed in the more general assumption, "All men are mortal"; that we can not be assured of the mortality of all men, unless we are already certain of the mortality of every individual man... That, in short, no reasoning from generals to particulars can, as such, prove anything, since from a general principle we cannot infer any particulars but those which the principle itself assumes as known. (from his A System of Logic. Book 2, Chapter 3, Section 2.)



Do you agree? Why or why not?

I do not agree because a Petitio Principii is a generality. The structure of the argument contradicts the answer.

Interesting subject by the way, I understand why most people would not respond...it is over most people's heads.

[Empiricist-Bruno]

What if it said, "All men are immortal"? Then Socrates is not a man.

The point of logic is not to obtain the truth but to avoid contradictory statements. Logic apparently has nothing to do with reality.

[Eodnhoj]

What if it said, "All men are immortal"? Then Socrates is not a man.

The point of logic is not to obtain the truth but to avoid contradictory statements. Logic apparently has nothing to do with reality.

Avoiding contradiction is observing definition as proportionality/ratios. All contradictions are a deficiency in ratios. To argue against the necessity of observing proportionality is to argue against justice itself.

In regards to the statement "All men are immortal" would imply that no men exist to make the statement. The function of the statement contradicts the form of the answer.

[Eduk]

All men are mortal, Socrates is a man, therefore Socrates is mortal;

Can't see anything wrong with the logic of this?
All men are mortal, Socrates is mortal, therefore Socrates is a man; This is a syllogism right?
Socrates is moral, Socrates is man, therefore All men are mortal; This does not follow either, this seems to be John Stuart Mill's point? I am probably misunderstanding something here?
I don't agree that every single man must be proven to be mortal (presumably by killing them) to come to the conclusion that all men are mortal. If that is the point being made?
That seems like a particular kind of philosophical pointlessness to me. A way of proving logic is illogical by using logic, where all the evidence points to the contrary.

-- Updated April 11th, 2017, 11:02 am to add the following --

Socrates is moral, Socrates is man, therefore All men are mortal

sorry typo meant to write
Socrates is mortal, Socrates is a man, therefore all men are mortal

[Fooloso4]

I think Cindycakes was hoping for help with her homework.

I think this is where the argument fails:

we can not be assured of the mortality of all men

Unless there is some reason to doubt it, this need not come into question unless the goal is to demonstrate absolute certainty. I see it as a formalized rule of reason by which we can draw conclusions about a particular (Socrates) based on knowledge of the general (all men). It is a practical and useful rule of reason,

I disagree, however, with those who see the syllogism only in propositional terms. In many cases it is not even articulated. It is seeing this is one of these.

[Empiricist-Bruno]

What if it said, "All men are immortal"? Then Socrates is not a man.

The point of logic is not to obtain the truth but to avoid contradictory statements. Logic apparently has nothing to do with reality.

Avoiding contradiction is observing definition as proportionality/ratios. All contradictions are a deficiency in ratios. To argue against the necessity of observing proportionality is to argue against justice itself.

In regards to the statement "All men are immortal" would imply that no men exist to make the statement. The function of the statement contradicts the form of the answer.

I have made the statement: "All men are immortal."
Eodnhoj makes the statement: "No men exist."
The logical conclusion is that "All fictitious men are immortal."

That make sense, doesn't it? Anyone can make any other statement and we'll see if we can find a system logic to it that will dodge contradictions. I'll call that logic.

[Eodnhoj]

I have made the statement: "All men are immortal."
Eodnhoj makes the statement: "No men exist."
The logical conclusion is that "All fictitious men are immortal."

That make sense, doesn't it? Anyone can make any other statement and we'll see if we can find a system logic to it that will dodge contradictions. I'll call that logic.

It makes sense but I believe, and correct me if my memory fails, that your example is a Hegelian synthesis of perspectives...I would agree it is logic as a degree of logic (as logic is multifaceted), but not the totality of logic.

All one could come to the conclusion:

"No men are immortal" = "All fictitious men are immortal"
"Possibly there is no immorality as there are no immortal men"
"Possibly immorality is a fiction"
"Immortality is told in fictions"
"There are rational observers that are not man"
"Fictions are a byproduct of non-human entities."
"All immortal men do not exist in this dimension."

or:

"All men are immortal" is a lie or taken out of context.
"No men exist" is a lie or taken out of context.

The point I am trying to make is that these statements, and we will call them "axioms", manifest as much definition as to the axioms they are relative to, reflective with, and/or synthesizing with. A low degree of argument definition is congruent with a low degree of axiom definition.