Begging the Question

[JOZeldenrust]

I'll try to explain the basics of first order logic. ...

Thanks, but I think I'll stick to Irving M. Copi's Introduction to Logic and Symbolic Logic. I don't know why, but someone who sees a significant semantic difference between 'assumption' and 'premiss' does not appeal to me as a source to learn the basics of logic from.

He'll tell you the same thing.

Oops, he might not. Seems like terminology varies between schools. The way I've been taught is to call temporary premisses "assumptions".

Proofs can be nested. Premisses are assumptions on the highest level of the argument. Within the argument, you can have partial proofs. In a partial proof, you can introduce one extra assumption, and you can use all propositions you can also use in the main proof. By the end of the partial proof, you have to drop the introduced assumption, but it's often possible to derive something from it nonetheless. See above for an example. It's a proof for one of the two rules of DeMorgan. Look them up. They are

1: - (A or B) -> (-A and -B)
2: - (A and B) -> (-A or -B)

Any introduction to logic should have those examples. Compare them to my proof. Then decide if I'm a reliable source.

[Hermit]

The way I've been taught is to call temporary premisses "assumptions".

And "permanent premisses" are more correctly known as axioms.

The people who taught you this kind of stuff should be fired. If they can't be sacked because they are tenured, the university should be closed down. Had they taught you about the healing powers of pyramids, they wouldn't have done much worse.

[JOZeldenrust]

The way I've been taught is to call temporary premisses "assumptions".

And "permanent premisses" are more correctly known as axioms.

The people who taught you this kind of stuff should be fired. If they can't be sacked because they are tenured, the university should be closed down. Had they taught you about the healing powers of pyramids, they wouldn't have done much worse.

I went back and checked my books. Turns out I was wrong. They didn't in fact have different terms for assumptions in the main proof and assumptions in partial proofs. They were all just called assumptions. I got confused because it was customary te describe proofs by their conclusion, the number of assumptions in the main proof, and the minimum number of steps required to derive the conclusion. In such a description, the assumptions were called premisses. The proof for the rule of DeMorgan I gave above would be:

"a proof of ( - ( A / B ) -> ( -A + -B ) ) from zero premisses/assumptions in eleven steps."

That doesn't make what I said nonsense. I just confused some terminology, like thinking the right thy bone is called the thy bone, and the left thy bone is called the femur.

I wasn't talking about axioms. Axioms are assumtions about the theory, that can't be derived from other axioms or from nothing at all. In first order logic, the properties of at least two connectives (either negation and conjunction or negation and disjunction) are axioms. The other two connectives can be expressed in terms of the first two:

A -> B is equivalent to - ( A + -B ) or ( -A / B)
A + B is equivalent to - ( -A / -B )
A / B is equivalent to - ( -A + -B )

So I confused terms. I thought there was a semantic difference where there wasn't one. What I should've said was "assumptions in the main proof" where I said "premiss" and "assumption in a partial proof" were I said "assumption".

[JOZeldenrust]

I'm going to get a little mean now, and list all the nonsense you've spouted in this thread:

"all humans are mortal" must include all humans called Socrates.

Not until line two, which introduces the minor premiss, to wit: Socrates is human. Please stop ignoring the fact that the the conclusion follows from two separate and independent premisses, the first one proposing that all humans are mortal, and the second one proposing that Socrates is human. If either one is wrong, the conclusion is falsified because of it. Thus, no circularity - or begging the question - in this syllogism. Socrates is definitely mortal only if both premisses obtain. The conclusion that Socrates is mortal depends on both aforementioned premisses being true: 1. All men are mortal, and 2. Socrates was a man.

The conclusion isn't falsified by either premiss being false, it just doesn't follow from the premisses. Compare:

p1. All humans are mortal
p2. Socrates is my rabbit
c. Socrates is mortal

The conclusion doesn't follow from the premisses, but it may very well be true nonetheless. Or:

p1. All humans die before they're 100 years old
p2. Socrates is human
c. Socrates died or will die before he was/is 100 years old

The conclusion follows from the premisses, the conclusion is true, the major premiss isn't.

I've just proved that a white man is black!

You have done no such thing. The argument goes:
Premiss one: All men are black.
Premiss two: Socrates is a man.
Conclusion: Socrates is black.

Now, you do know what a premiss is, don't you? Yes, it is something you propose and if what you propose is wrong, the conclusion is wrong. So, we may say (once again): If all men are black and if Socrates is a man, then Socrates is black. Only one of the two premisses would need to be wrong for the conclusion to be invalid. If you look at premisses as conditional statements - which is what they are in symbolic logic - the issue of circularity (begging the question) flies out the window.

No, if what you propose is right, then your conclusion must be right. If one of the premisses is wrong, you can't use the argument to show that the conclusion is either right or wrong.

Is this begging the question?
p1: All planets orbit the sun
p2: mars is a planet
C.: mars orbits the sun

Not begging the question. The argument is short for: If all planets orbit the sun and if Mars is a planet, then Mars must be orbiting the sun. In other words, if - and only if - the premisses are true, the conclusion must necessarily follow.

Is this begging the question?
p1: mercury, venus, earth, mars, jupiter, saturn, uranus, neptune and pluto orbit the sun
p2: mars is a planet
C.: mars orbits the sun

That is not even a properly constructed syllogism. The last line is not a conclusion. It is a reiteration of premiss 1: And, yes, that is begging the question.

It's not a syllogism, but the last line is a conclusion that follows from the premisses.

p1: Mars orbits the sun
c.: Mars orbits the sun

is a sound argument. It's completely useless, but it's sound. In formal logic, there is no such thing as begging the question. There's only a non sequitur. Begging the question is a specific retoric form that a non sequitur can have. It's called begging the question, because an assumption is left implicit. If you write out the proof in formal logic, either you omit the implicit assumption, and it's a non sequitur, or you introduce the formerly implicit assumption into the premisses, and you have a logically sound argument. Of course, you'd still have to defend the truth of all your premisses.

It's not a tautology either, by the way. A tautology is a proposition that can be derived without any assumptions. ( A or -A ) is a tautology.

p1: Mars orbits the sun
c.: Mars orbits the sun

follows from one premiss, so it's not a tautology. If a proof is sound, conjugating all premisses and having them imply the conclusion results in a tautology. So "If all men are mortal, and Socrates is a man, then Socrates is mortal" is a tautology.

That is not even a properly constructed syllogism. The last line is not a conclusion. It is a reiteration of premiss 1: And, yes, that is begging the question.

I'd say its a tautology, as its says mars orbits the sun therefore mars orbits the sun.

Synonymous, ain't it?

Absolutely not. Tautologies are always true. "Mars orbits the sun therefore mars orbits the sun" depends on the premiss. The fact that the conclusion is a repetition of the premiss makes it a useless proof, but it is sound.

In other words, Seraph, you're making at least as big a mess of your terminology as I am, and you show a poor grasp of logic to boot. It's better then MisterMack's, I'll give you that, but you still have no business lecturing me about logic.

[camoguard]

Anybody who says this

p1: All planets orbit the sun
p2: Mars is a planet
p3: The moon is a planet
C.: Mars orbits the sun

is fired from talking about logic.

In the case quoted, we can see several things wrong with the example. The moon isn't a planet. Also, the moon's status as a planet can be checked against premise 1. Most egregiously, the moon's status as a planet is meaningless to the argument unless it were true in which case the conclusion would be that all planets do not orbit the sun.

You're fired JOZeldenrust. Stop tainting my logic thread.

[JOZeldenrust]

Anybody who says this

p1: All planets orbit the sun
p2: Mars is a planet
p3: The moon is a planet
C.: Mars orbits the sun

is fired from talking about logic.

In the case quoted, we can see several things wrong with the example. The moon isn't a planet. Also, the moon's status as a planet can be checked against premise 1. Most egregiously, the moon's status as a planet is meaningless to the argument unless it were true in which case the conclusion would be that all planets do not orbit the sun.

You are introducing empirical knowledge into a logical argument. Empirical knowledge is inductive, logical arguments are deductive. Keep things straight, please.

Within the context of this proof, the moon being a planet is assumed to be true, so within this proof, it's possible to derive "the moon orbits the sun", and that would be a valid conclusion.

You were insisting that logic is about form. Formally, this argument is sound. If all premisses are true, the conclusion must be true. Not all premisses are true (that was the point of the example), but regardless, the conclusion is true. In logic, whether or not the premisses are empirically true is irrelevant. Premisses are assumed to be true within the context of the proof. From p1, p2 and p3, C follows.

C follows from just p1 and p2 as well, but that doesn't matter.

You're fired JOZeldenrust. Stop tainting my logic thread.

Learn to read, chump.

Jesus, am I the only one who gets logic on this entire forum?

[camoguard]

A logical argument that doesn't have all it's pieces making sense can't be right man. Inserting erroneous premises is wrong. Your conclusion ceases to follow.

[camoguard]

Let me rephrase. Your argument is logically valid. However, we can spot the false premise and there's got to be some terminology for logic that uses too many premises, you're doing that there.

I did find this

Begging the Question

An argument begs the question when it makes use of a premise that no one who didn't already accept the conclusion would believe. Simply put, an argument begs the question when it reasons in a circle or presupposes the truth of the very thing it's trying to prove.

which was helpful. The socrates example still doesn't beg the question to me. Nor does the planets argument.

[JOZeldenrust]

Let me rephrase. Your argument is logically valid. However, we can spot the false premise and there's got to be some terminology for logic that uses too many premises, you're doing that there.

As far as I know there isn't. Generally, people consider it a good thing to strive for parsimony (having as few premisses as neccesary), but that's not a part of logic. It's an aesthetic principle without objective basis. It's generally known as Occam's razor. The fact that it doesn't have an objective basis doesn't make it a bad thing, though. Keeping things as simple as possible is good practice.

I did find this

Begging the Question

An argument begs the question when it makes use of a premise that no one who didn't already accept the conclusion would believe. Simply put, an argument begs the question when it reasons in a circle or presupposes the truth of the very thing it's trying to prove.

which was helpful. The socrates example still doesn't beg the question to me. Nor does the planets argument.

Indeed. Thing is, though, that in the context of formal logic, the term "begging the question" is meaningless. In formal logic, something is either a valid argument or a non sequitur. "Begging the question" refers to certain retoric forms that a non sequitur can have (or you could consider "begging the question" to be using a premisse that is both implicit and false, in which case the argument isn't a non sequitur, but still unsound, but that approach again goes outside the boundaries of formal logic), and retoric forms aren't part of formal logic.

[mistermack]

In other words, Seraph, you're making at least as big a mess of your terminology as I am, and you show a poor grasp of logic to boot. It's better then MisterMack's, I'll give you that, but you still have no business lecturing me about logic.

I have no interest in the "correct terminology", but I do recognise a load of bollocks when I read it, and this thread is full of it.
That's where your terminology is wrong. Calling this shit "logic".
Use the correct term, bollocks, and it all makes sense.
.

[Rob]

Joz, you admitted that Begging the question has no place in formal logic and then continue to criticize points of view in this thread about begging the question. If this is a non-sequiter and thus a non-factor then why the hell are you talking about formal logic beyond saying that this question is irrelevant?

Mistermack, this thread has led me to two conclusions. You are either an idiot or a troll. There is no other possibility.

[Hermit]

Mistermack, this thread has led me to two conclusions. You are either an idiot or a troll. There is no other possibility.

That is one conclusion.

True or not, saying that another member is "either an idiot or a troll" is also against the rules.

Note: My withdrawal from this discussion is due to family matters making this issue look incredibly insignificant. Suffice it to say - JoZeldenrust - I don't think you are being mean to me at all. You were doing little more than to disagree with what I said. I just can't be bothered with this stuff right now.

[mistermack]

Mistermack, this thread has led me to two conclusions. You are either an idiot or a troll. There is no other possibility.

Rob, I've given my reasoning on this thread in detail, you just come out with meaningless slagging-off. Playground stuff. Pathetic. Like many others, you're scared to make a specific criticism, because you don't want to look silly. It's not working.
.

[mistermack]

Just to repeat what I've said in earlier posts, these various "disciplines" of formal "logic" were discredited long ago. That's why they are bollocks. Especially if you insist on calling it logic.
The word logic may have applied thousands of years ago, but logic has a different meaning now. There may be logic involved in it, but there's plenty of rubbish too.

Now it's a bunch of rather odd people playing with antique tools that don't work. Hence we have arguments which are technically correct, and of no value whatsoever.
That applies to practically all of it.
And that's my definition of bollocks.
.

[JOZeldenrust]

Just to repeat what I've said in earlier posts, these various "disciplines" of formal "logic" were discredited long ago.

Care to explain how formal logic has been discredited?

That's why they are bollocks. Especially if you insist on calling it logic.
The word logic may have applied thousands of years ago, but logic has a different meaning now. There may be logic involved in it, but there's plenty of rubbish too.

Now it's a bunch of rather odd people playing with antique tools that don't work. Hence we have arguments which are technically correct, and of no value whatsoever.

Logic is a tool. On its own, it doesn't do anything. It's only for examining the structure of arguments, not for the content.

That applies to practically all of it.
And that's my definition of bollocks.
.

The kind of logic I'm using isn't that old: most of it was thought up by Frege, in his 1879 publication "Begriffschrift".