Evidence for atheism

[Jackalope]

Not in any traditional sense, no. The classic syllogism has exactly 3 statements: if p then q, p, q. The entire syllogism is not a statement.

How is that not a statement? How can we separate any part from another and make such a statement?

If -not p- then what? If I plug that in, in place of your "if p" what happens?

It's not a statement within the realm of classical logic.

In logic a statement is either (a) a meaningful declarative sentence that is either true or false, or (b) that which a true or false declarative sentence asserts. In the latter case, a statement is distinct from a sentence in that a sentence is only one formulation of a statement, whereas there may be many other formulations expressing the same statement.

In your example, if not-P is indeed true, then we can deduce not-Q. That still doesn't alter in any meaningful way what I've been saying. If you've got an actual argument in that form, by all means, let's dissect it.

[The Grand Nudger]

It's not a statement within the realm of classical logic.

No shit...lol, I should have been more precise (and I forget sometimes that people better educated than I approach this with standardized and classical terminology from the realm of philosophy - rather than machine logic), mea culpa "not p" was a poor choice of words on my part, I was describing a state, not a rule of inference. "Not p" in the context of a statement which might be made by...say, a creationist. As in, "If such and such is true, than" whereby you state "such and such is not true". The requirement that each component be sound-and the designation of some component as not being sound.

[Angrboda]

The following invalid argument in natural language:

If a, b;
c;
therefore b.

is represented sententially as:

((( a ⇒ b) Λ (c)) ⇒ b )

This statement as a whole is false; we can conclude nothing about (b) as an independent proposition. Moreover, we can use this sentence as a whole in another proposition in place of the value FALSE and order is preserved, and any argument based on that is valid and sound with respect to this part of the syllogism, no matter how we transform the original statement via the laws of logic. However, substituting b for FALSE is not an order preserving operation and any arguments formed from doing so are for that reason invalid and result in a non sequitur.

[Jackalope]

It's not a statement within the realm of classical logic.

No shit...lol, I should have been more precise (and I forget sometimes that people better educated than I approach this with standardized and classical terminology), mea culpa "not p" was a poor choice of words on my part, I was describing a state, not a rule of inference. "Not p" in the context of a statement which might be made by...say, a creationist. As in, "If such and such is true, than" whereby you state "such and such is not true". The requirement that each component be sound.

OK so I think the source of our mutual confusion has become apparent.

So you're asking about this:

If P then Q
Not P
Therefore, not Q.

That's a fallacy of the inverse (denying the antecedent)

[The Grand Nudger]

No, no no, I don't think that any of us are unclear on the rules. Reach back to the point at which we went on our excruciatingly specific exploration of the topic.

I'm confident in stating that the "god conclusion" is false. I'm explaining my confidence - thus, my confusion when others say "we cannot know" or, if you prefer, allowing the possibility of god on a technicality.

I say that we can know, and here's why

If p, then q
p
therefore q

That describes the rules.

If ants are 5 feet tall, then god
ants are 5 feet tall
therefore god.

The operator here, implied in the statement - in the very act of "doing logic" what makes it "true" -because ants are 5 feet tall, god-

What happens when I mention that ants are, in fact, not 5 feet tall?
(ignore the ridiculous premise, obviously)

.........also...Rasetsu!...how did you enter those implication signs?

[Angrboda]

Nothing happens. The entire argument as a whole is false. But the conclusion is unknown from anything that has come before.

[Jackalope]

No, no no, I don't think that any of us are unclear on the rules. Reach back to the point at which we went on our excruciatingly specific exploration of the topic.

I'm confident in stating that the "god conclusion" is false. I'm explaining my confidence - thus, my confusion when others say "we cannot know" or, if you prefer, allowing the possibility of god on a technicality.

I say that we can know, and here's why

If p, then q
p
therefore q

That describes the rules.

If ants are 5 feet tall, then god
ants are 5 feet tall
therefore god.

The operator here, implied in the statement - in the very act of "doing logic" what makes it "true" -because ants are 5 feet tall, god-

What happens when I mention that ants are, in fact, not 5 feet tall?

If you attempt to conclude that by that virtue, god does not exist, you are committing a formal fallacy.

[The Grand Nudger]

I'm concluding that the god who exists -because ants are 5 feet tall- does not exist.

[Jackalope]

I'm concluding that the god who exists -because ants are 5 feet tall- does not exist.

If the queen of England is a U.S. citizen, she is human.
She is not a U.S. citizen.
She is not human.

QED

[The Grand Nudger]

Is the premise sound? Is the argument valid?