Begging the Question

[darren]

A long time since I have visited this thread. Thanks for the discussion. I have another related question, if you are interested. For simplicity, Lets pretend that it is 1990 and no exoplanets have been discovered.

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

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

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If you give two different answers, why?

[leo-rcc]

Case 1 is not begging the question.

Case 2 The conclusion is Tautological, P1 states Mars orbits the Sun, and the conclusion is Mars orbits the Sun. Premise 2 has no bearing at all to the conclusion.

[Hermit]

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.

[leo-rcc]

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.

[Hermit]

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?

[camoguard]

"Begging the Question" is a stupid thing to say even when you think you know what question is being begged.

Raise your hand if you think formal logic is stupid. I'm going to need a separate volunteer to take those identified people out back and have them sterilized. No, don't raise your hands to volunteer. Thanks.

I agree with what has been said before about the two different cases. Listing the planets is different than saying "all planets" because saying "all planets" hints that what you mean to say is you observe a pattern of all planets orbiting the sun or that you've read a definition that planets are celestial objects that orbit the sun. Then later you notice Mars is a planet perhaps by reading about it and can reasonably be expected to understand it orbits the sun. The first example makes sense.

The second example is a case where the writer obviously forgot that they already knew that Mars orbited the sun.

[JOZeldenrust]

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?

Nope, a tautology is a valid argument, begging the question isn't. When begging the question, the conclusion isn't part of the premisses, it's part of the assumptions. This gets a bit confusing, because usually the assumption is implicit. You'd get something like:

1. Mercury, Venus, Earth, Jupiter, Saturn, Uranus and Neptune are planets (p1)
2. All planets orbit the sun (p2)
3. |Mars is a planet (a1)
4. |All planets orbit the sun (rep2)
5. |Mars orbits the sun (elimination of universal quantor using 3,4)
6. Mars orbits the sun (begging the question)

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.

Nope, the premisses don't have to be true for the conclusion to be true. Compare:

p1: All planets orbit the sun
p2: Jupiter is a planet
C.: Mars orbits the sun

All premisses are true, but the conclusion doesn't follow from the premisses. The conlusion is still true. Or:

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

Not all premisses are true, the conclusion does follow from the premisses, and the conclusion is true.

[darren]

(pre-1990)
p1: All planets orbit the sun
p2: mars is a planet
C.: mars orbits the sun

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


why is one syllogism question-begging, and one not, when they are the same argument? I have simply replaced "all planets" with a synonym (mvemjsunp)?
either they are both question-begging or they are both not question-begging?

[JOZeldenrust]

(pre-1990)
p1: All planets orbit the sun
p2: mars is a planet
C.: mars orbits the sun

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


why is one syllogism question-begging, and one not, when they are the same argument? I have simply replaced "all planets" with a synonym (mvemjsunp)?
either they are both question-begging or they are both not question-begging?

Neither are begging the question.

Why are you going about this in formal logic? In formal logic there's no such thing as "begging the question", there's only a non sequitur. "Begging the question refers to the specific retoric form in which the unsound argument is presented. Remove "Mars" from p1 in your second argument, and you have a non sequitur. This could be presented as begging the question:

Mercury, Venus, earth, Jupiter, Saturn, Uranus, Neptune and Pluto orbit the sun. Mars is a planet, so Mars orbits the sun.

Your two arguments aren't the same, by the way,: the first argument requires both premisses to be true for the conclusion to follow from it. The second argument only needs the first premisse. Explaining the difference is a bit hard. It has to do with the fact that "all" is a weird little word in syllogism logic. You'd need first order logic to solve this. First order logic uses quantors, two of them: the existential quantor, and the universal quantor. In most cases, the word "all" translates to the universal quantor, but things get weird when you introduce negations.

[Hermit]

When begging the question, the conclusion isn't part of the premisses, it's part of the assumptions.

Oh, purleeease!

[JOZeldenrust]

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

In first order logic, you work with propositions. They consist of names, name functions, identity, sentences, sentence functions, connectives and quantors.

Names are the simplest entities, but I'm going to start with name functions. Name functions denote things. Every name function has a number of places. A name function that has no empty places is a name. Places in a name function can be filled by names.

Examples:

Three zero place name functions: Alice, Bob, Carol, let's call these "a,b and c"
Two one place name functions: The father of ..., the mother of ..., lets call these "f and m"
A two place name funtion: The child of ... and ..., let's call this one "o"

With these name functions, you can create an infinite number of new names:

"f(a)", the father of Alice; "f(b)", the father of Bob; "m(f(c))", the mother of the father of Carol; "o(m(c),f(f(a)))", the child of the mother of Carol and the father of the father of Alice, etc.

A name function with unfilled places in a proposition is considered ill formed.

Identity denotes that two names refer to the same thing. I'll use "=" to denote identity.

Examples:
b = f(a), translation: Bob is the father of Alice
a = o(c,m(a)), translation: Alice is the child of Bob and the mother of Alice

Sentences functions denote a state of affairs. Like name functions, they have a number of places. These places can be filled by names. If all places of a sentence function are filled, it's a sentence.

Examples:

A zero place sentence function: It's raining, let's call this "R"
A one place sentence function: ... is hungry, let's call this "H"
A two place sentence function: ... kisses ..., let's call this "K"
A three place sentence function: ... is standing between ... and ..., let's call this "B"

With these sentence functions and name functions, you can create an infinite number of sentences:

"H(a)", Alice is hungry; "K(a),f(c))", Alice kisses the father of Carol; "B(m(c),c,a)", the mother of Carol is standing between Carol and Alice, etc.

A sentence function with unfilled places in a proposition is considered ill formed.

Connectives denote logical relationships between sentences. There's only a limited number of them:
The conjugation (logical "and"), is true if both conjugated sentences are true. I'll use "+" to denote conjugation.
The disjunction (logical "or"), is true is at least one of the disjointed sentences is true. I'll use "/" to denote disjuction.
The negation (logical "not"), is true if the negated sentence is false. I'll use "-" to denote negation.
The material implication (logical "if"), is true if the first sentence is false, or both sentences are true. I'll use ">' to denote implication.

The material implication can be a bit confusing. Take the following proposition:

"H(a) > B(b,f(b),m(b))" translation: if Alice is hungry, then Bob is standing between the father of Bob and the mother of Bob.

If "H(a)" is true, and "B(b,f(b),m(b))" is true, then "H(a) > B(b,f(b),m(b))" is true.
If "H(a)" is true, and "B(b,f(b),m(b))" is false, then "H(a) > B(b,f(b),m(b))" is false.
If "H(a)" is false, and "B(b,f(b),m(b))" is false, then "H(a) > B(b,f(b),m(b))" is true.
If "H(a)" is false, and "B(b,f(b),m(b))" is true, then "H(a) > B(b,f(b),m(b))" is true. (this one is a bit counter-intuitive)

That leaves the quantors. There are two of the. The existential quantor, which denotes that something exists, and the universal quantor, which denotes that a sentence applies to everything in the domain of the logical language you've created. I'll use "%" to denote the existential quantor, and "@" to denote the universal quantor.

Examples

Let's choose "everything" as our domain. What if you'd want to say "there exists a child of Alice and Bob, and that child is hungry". You'd need the existential quantor: %x(o(x,a,b) + H(x)). Now let's suppose you'd want to say that all children of Alice and Bob are hungry. Then you'd need the universal quantor: @x(o(x,a,b) > H(x)). It gets a bit more complicated if you want to negate these proposition. Let's say you'd want to say "none of Alice's and Bob's children are hungry. You'd think that's just a negation of the second proposition, but it isn't. It actually means that there are no children of Alice's and Bob's who are hungry. You could translate this sentence as "-%x(o(x,a,b) + H(x)) or "@x(o(x,a,b) > -H(x))".

That's the tools out of the way, in my next post I'll get to the rules of introduction and elimination of the connectives.

[Hermit]

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.

[JOZeldenrust]

When begging the question, the conclusion isn't part of the premisses, it's part of the assumptions.

Oh, purleeease!

In formal logic, the two aren't the same. An assumption is a temporary premisse that must be abandoned before the end of the argument. It's used in what is called a "partial proof", which are important in deriving true proposition.

Code: Select all

1.  | - (A / B)             (assumption, beginning of partial proof (p), after the horizontal line the assumption is discarded)
2.  | | A                   (assumption, again, this time a part of a partial proof (q) within partial proof(p))
3.  | | (A / B)             (introduction of a disjunction in 2)
4.  | |_X___________________(contradiction, from the assumption in 2 follows a contradiction with the assumption in 1, end of partial proof(q))
5.  | -A                    (because ass. 2 leads to a contradiction with ass. 1, the negation of 2 is true, at least within partial proof(p))
6.  | | B                   (assumption, again, this time a part of a partial proof (r) within partial proof(p)
7.  | | (A / B)             (introduction of a disjunction in 6)
8.  | |_X___________________(contradiction, from the assumption in 2 follows a contradiction with the assumption in 1, end of partial proof(r))
9.  | -B                    (because ass. 6 leads to a contradiction with ass. 1, the negation of 6 is true, at least within partial proof(p))
10. |_(-A + -B)_____________(introduction of a conjunction of 5 and 9, end of partial proof(p))
11. - (A / B) > (-A + -B)   (because 10 can be derived from 1, it can be concluded that 1 > 10)

(copy the text into wordpad to restore the lay-out)

There, proof of a (tautological) proposition, derived from zero premisses, using several assumptions in partial proofs.

[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.

[Hermit]

An assumption is a temporary premisse...

...and a premiss is something that is assumed.