Syllogistic Proof

[Fangrim]

Nothing can be proven unless two premises are assumed true.

Discuss.

[Alive]

Nothing can be proven even if two premises are assumed true. More specifically, an infinite number of premises have to be assumed true to make a proof; including unstated premises (that is, you can never state all the premises you must assume to prove something.)

[5010]

What about this?

Frank is inside the house.
Therefore: Frank is smaller than the house.

[gallo]

Quote by: Alive Nothing can be proven even if two premises are assumed true. More specifically, an infinite number of premises have to be assumed true to make a proof; including unstated premises (that is, you can never state all the premises you must assume to prove something.)

He specifically said, "Syllogistic Proof." It is basic logic and he is correct given that the form of the syllogism is correct. For example:

All horses have 4 legs
That animal has 4 legs
Therefore, that animal is a horse.

is incorrect even if both premises were true.

Nothing is better than heaven
Half a loaf is better than nothing
Therefore, half a loaf it better than heaven.

The form is correct, and if you accept both premises, it is still invalid since 'nothing' is used with two different definitions.

By the way, in logic, the syllogistic arguments are known as proofs. Any other premise is irrelevant if you accept the two in any argument as true.

[Alive]

gallo,
In traditional logic, one doesn't need two stated premises to prove something. For example, identity follows without any premises at all! Less trivially, we can "prove" the law of excluded middle without any premises, because it follows from only the basic axioms of logic (and logic differentiates arbitrarily between premises and axioms).

But all proofs have unstated premises/axioms necessary to actually make the proof. Take the "correct" form of your first syllogism:

1. All horses have 4 legs
2. That animal is a horse
3. Therefore, that animal has 4 legs.

Prove that 1 and 2 imply 3! What logical basis do you have for believing that 1 and 2 imply 3? You need another premise, of the form: If all horses have have 4 legs, then any animal that is a horse has 4 legs. (You might find this premise silly given the conclusion, and try to come up with a more general axiom relating the specific to the general, but that is irrelevant towards are essential problem).

Our new proof:

1. All horses have 4 legs
2. That animal is a horse
3. If all horses have 4 legs, then any animal that is a horse has 4 legs
4. Therefore, that animal has 4 legs

Ah, now prove that 1 and 2 and 3 imply 4! You need another premise. :) This can go on forever, hence you need infinite premises to make a proof. The argument that any proof also needs unstated premises will wait for later.

[5010]

An example of proof requiring no premise:

This sentence is written.

[Cephus]

Quote by: 5010 An example of proof requiring no premise: This sentence is written.

No it wasn't, it was typed. Statement disproven.

[5010]

Quote by: Cephus No it wasn't, it was typed. Statement disproven.

Look up type in the dictionary.

type, verb- 1. write by means of a keyboard with types; "type the acceptance letter, please"

[triad]

Complicated.:eek:

[Fangrim]

Quote by: 5010 What about this? Frank is inside the house. Therefore: Frank is smaller than the house.

Frank is inside the house.
If Frank is inside the house, then Frank is smaller than the house.
Therefore: Frank is smaller than the house.

You missed premise 2.

Quote by: 5010 An example of proof requiring no premise: This sentence is written.

Your actual syllogism:
That sentence [down there, the conclusion] exists.
If that sentence exists, it is written.
Therefore, this sentence is written.

[5010]

Fangrim,
"Frank is inside the house, therefore frank is smaller than the house" is the same as "if Frank is inside the house, then Frank is smaller than the house". That's just redundant and unnecessary (pun intended).

On the second one, it is completely self-evident to anyone who reads it and understand the words. No other information is required. Welcome to personal revelation :)

[chrisphd]

What about this:
"This text exists."

[Kamehameha34]

Quote by: chrisphd What about this: "This text exists."

That would follow thusly:

1. X
2. Therefore, X


That's not a syllogism, that's circular.